In a small bowl, combine the ingredients for the herbed mayonnaise. Season with salt and pepper to taste. Do Ahead: The herbed mayonnaise can be made up to a day in advance and stored in the fridge.
Set up a “dredging station.” Place the cornmeal, whisked eggs and panko breadcrumbs in separate shallow bowls or rimmed plates. Season each with salt and pepper.
Trim the fish fillets into sandwich-sized or slightly smaller pieces (I usually cut them in half, depending on how big they are). Season with salt and pepper.
Dredge the trimmed fish filets in the cornmeal (on both sides), followed by the whisked eggs, followed by the breadcrumbs. Place the breaded filets on a wax- or parchment-lined baking sheet while you heat up your skillet.
Heat the oil in a large, heavy cast iron or nonstick skillet over medium-high heat until shimmering and hot (you can add a pinch of breadcrumbs to test the oil—they should immediately start to sizzle). Working in batches, fry the fish for about 1-2 minutes per side, or until golden brown on both sides and cooked through.
Spread some of the herbed mayonnaise on 4 buns (I like to spread a thick layer on the bottom bun, and a lighter smear on the top bun, but that’s just me). Pile a couple of pieces of fish on each bottom bun, followed by a tomato slice, a few avocado slices and a leaf or two of lettuce. Crown the sandwiches off with the top buns, then devour. Hello summer.