I'm no expert and don't even have humongous legs, I'm just a guy who does a ton of research, so take what I'm about to say with a grain of salt.

Low Rep + High Weight = Strength Gains. Cool thing about being stronger is your muscles are going to get a little bigger and a lot thicker. Bad part is that everything gets bigger. If you're squatting super heavy for low reps, and you're increasing weight over time, you're going to be recruiting more than just that dominant middle quad muscle (I forget what it's called, but it's the big one we all want to grow the most), which means the entire leg is going to grow bigger and thicker. This is why power lifters are generally huge, but not necessarily cut; everything grew rather than just the glamour muscles. Hold onto this info, we'll get back to it in a moment.

High Reps + Low-But-Still-Challenging Weight = Hypertrophy, aka Making the Muscle Bigger. You do this, and muscles grow more, but don't necessarily get a lot stronger. Like the above paragraph, there's going to be some strength gains and hypertrophy gains in both methods, but each methods contributes significantly more to its respective goal. But going this method, thinking legs, your squat will predominantly use that primary quad head, and it's a more practical method for exercises like leg extensions which are designed to focus more on one head vs. the whole muscle group. Thus, you get definition.

Here's the really interesting part. That second paragraph about hypertrophy, it has much more meaningful gains in size if you use a heavier weight. And hypertrophy training isn't designed to get you to use a heavier weight, while the strength paragraph above does. This is why strength gains are still important even if your goal is purely for hypertrophy.

Here's an actual answer to your question. First off, most trainers are morons. Not saying yours is or isn't, but I've come to realize that we as a society know extremely little about this stuff, and trainers stop learning the moment they feel they're an expert; this means many of them are stuck in their dogmatic ways, and it's important for all of us to continue to learn new things that science reveals so we can 1) Apply new methods ourselves, and 2) Evaluate trainers and general advice givers (like me right now) to decide if they're total bullshit.

**Ok, I swear I'm going to answer your question now." If you want a bigger leg all around, low reps + high weight is the main way to go. The whole leg is going to get beefier. If you want definition, keep doing what you're doing, especially if you're on a cut. Ideally though, you'd eat a little more, focus on those low reps to increase strength, and then use that new strength to use higher weights on your 4x15 work. Rinse/repeat.

You said in the last sentence that your legs are beefy as hell but not cut at all. This probably means you're doing the right thing, if you want definition. You've got strength and overall size. The 4x15 work should maintain/possibly increase that main quad head, leaving any muscle atrophy that occurs during the cut to predominantly affect those other three heads. Combined with a decrease in body fat from cutting, the leg should look good by the end. Granted, it might decrease in size overall in general, again because of cutting and because you aren't doing a ton of strength training, but that's why we bulk/cut cycle.