Preheat oven to 375°F and position a rack in the center.
Lay tomato slices on paper towels. Sprinkle with 1 tsp salt. Rest 20 minutes, then blot dry.
Stir mayonnaise, cheddar, mozzarella, garlic, green onion, basil, pepper, Dijon, and remaining 1/4 tsp salt.
Dust the cooled prebaked crust evenly with the cornmeal.
Shingle half the tomatoes in the crust. Spread half the cheese mixture on top.
Repeat with remaining tomatoes and the rest of the cheese topping, sealing to the edges.
Bake until the top is golden and bubbly, about 30–35 minutes.
Cool 15–20 minutes before slicing. Serve warm or at room temperature.