Preheat oven to 350˚. Grease a medium cast-iron skillet with oil.
In a large skillet, heat 2 tablespoons oil over medium heat. Add onion; cook, stirring occasionally, until softened and caramelized, 12 to 15 minutes. Add tomatoes, torn basil, garlic, salt, and pepper.
Scatter 1 cup crushed crackers in prepared skillet. Pour tomato filling over crackers. Sprinkle with 1 cup crushed crackers.
In a medium bowl, combine mayonnaise, Cheddar, Parmigiano-Reggiano, and chopped basil. Spread mayonnaise mixture over crackers. Top with remaining ½ cup crushed crackers.
Bake until golden brown, 35 to 40 minutes.
Recipe by Louisiana Cookin' at https://louisianacookin.com/creole-tomato-pie/