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, if needed. Season each 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 (add a pinch of breadcrumbs to test the oil—they should immediately start to sizzle). Working in batches, fry the fish for about 1-3 minutes per side (depending on the thickness of the fish), or until golden brown on both sides and cooked through (keep your eye on the heat—if the fish is browning too quickly trust your instincts and turn it down). Transfer the fish to wire rack and season with salt.
Spread some of the Tarragon Aioli on 4 buns (I like to spread a thick layer on the bottom bun, and a lighter smear on the top bun). Arrange the fried fish on each 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.