Always ask for reviews. If you're getting lots of small jobs that means lots of new, happy customers. Make sure to ask them for reviews on Google and/or Facebook. Also, start advertising. If you are using a CRM for the small jobs you can use that audience list to create a 'similar audience' on Facebook for advertising. Also use Google Ads and create a campaign around your demographics and keywords that bigger jobs would represent. Good luck!

Mailing or door hanging of fridge magnet with lawn tips, which match up with services you offer.

Surprising how few people use magnets... which produce...

4745 impressions/year/person in household...

Cost is $1/magnet - magnet production + mailing cost, both of which are handled by magnet manufacturing company... so zero work on your part.

The answer is obvious: you add more sand...(to get to the next level). Sorry, I just had to, and humor is healthy right? :-)
On a more serious level:
1. The fact that you're doing lots of small jobs is already a good start (especially the "lots" part), because if you do a good job, clients will remember you, and one day, when they need a bigger job, you'll be the one they turn to.
2. Partner with someone to create a win-win situation. For example: when contractors build large housing projects, they often work with 1-2 large companies that design kitchens, and offer their services when they sell the houses to the buyers (before they're even built). These kitchen companies pay a percentage of their profits, or a one time fee, for this partnership. You could do the same: the contractor would offer the buyers your landscaping services (it's great moving in to a new house with an amazing garden) and the contractor would get a commission for each paying client.
3. One big project: big jobs require big properties and clients with money. Focus on getting one big client, offer him the project at almost nothing*, and then over deliver (do an amazing job). The discounted rate would be on the condition that they (1) give you a recommendation, (2) let you photograph the project and (3) recommend you to their friends. Just the fact that you completed such a project, will be of value when you pitch to other similar status clients.
4. Online targeted advertising - create a well designed website (you can do this for a rather cheap price on Fiverr), add pictures of your best projects, and advertise to your target market. Try be original: example: go to a place that needs some work done (perhaps a neglected public area), and create something amazing - and then leave a funny sign with your details. You might even get some media attention (just be sure you're not doing anything illegal).
I've successfully helped over 300 entrepreneurs and businesses and I'd be happy to discuss other marketing methods if you need to.
Good luck

If you're getting a lot of small jobs - congrats! That means you have a lot of customers who know your value and are willing to hire you.

That said, I TOTALLY get the desire to want to have fewer clients to manage, at a higher price point per project.

The first thing I'd have you ask yourself is this: Who are the people who would hire you for the kind of bigger jobs you're after?

Are they homeowners in more affluent neighborhoods? Development companies building new neighborhoods? Businesses who want their grounds to look nice for visitors?

Identify who they are, and put yourself in the same rooms as them. Find the kind of events they go to, and go to them to. Print of business cards that are more focused on the longer-term projects you'd like to have, rather than the smaller, one-off projects you're currently getting.

And leverage your testimonials. If you're continually landing lots of jobs, that tells me that people are happy with your work. If you don't yet have testimonials, ask your previous clients to give you some. Putting these on your website or on your other printed marketing material can go a LONG way in showing a new target market you're trying to break into that you're trustworthy and someone they'll want to hire.

That depends on what you mean by “next level”. I’d tend to focus on the jobs that create steady recurring revenue such as the maintenance contracts. Start asking your existing raving fans if anyone they know could use your help as well. Include a flyer in their invoice if you mail them. Send a text or email campaign that’s not spammy with a reward for referrals such as a coupon or free month of service.

Look for opportunities to automate or outsource some areas of your operations so you can work ON your business (market and sell) instead of IN your business (managing day to day). There’s always risk when you expand so make sure you have the cash on hand to deal with some unexpected challenges and be cautious not to over extend on any strategy. Hope this is helpful!

Train multiple prospects and create a team that can do the small jobs. You will find it gives you more time to work on your contract jobs and what ever you choose.

Find a local BNI group in your area that has complementary professions (residential cleaning, interior design, security systems, realtor). BNI is a commitment and requires a significant investment to join. But for you it may be well worth it, especially if you tap into the trainings BNI offers. You will build your skills in everything from identifying potential clients (beyond "someone who needs landscaping") to public speaking to developing strategic relationships.

How do you define “the next level“? Start with asking your current customers for referrals. If you are serious, offer them a discounted or free service for every neighbor they refer. I guarantee they will start talking to their neighbors about their yard guy.

If you are interested in more commercial projects, your best bet is to make friends with those in the industry. Many times, smaller commercial projects are owned by individual investors. By searching through public record, you can often identify their holding companies and spot clusters of small commercial units in a geographical area. Getting one of these often leads to servicing their entire portfolio.

All the best,
Shaun