Make the remoulade sauce: Whisk all of the sauce ingredients together in a small bowl until combined. Cover and refrigerate until ready to serve.
Stir 1/3 cup of the flour, salt, and paprika together in a wide, shallow bowl or pie plate.
Whisk the buttermilk, egg white, and hot sauce together in second wide, shallow bowl.
Stir the cornmeal and remaining 1/3 cup flour together in a third wide, shallow bowl.
Dip each tomato slice in the flour mixture, followed by the buttermilk mixture, and finally the cornmeal mixture.
Let the breaded tomato slices sit, so the coating sets while the oil heats.
Heat the oil in a large cast iron skillet over medium-high heat until shimmering, about 5 minutes.
Carefully add 4 to 5 tomato slices and fry until golden-brown, 3 to 4 minutes per side. Transer the fried tomatoes to a paper towel-lined plate. Fry the remaining tomato slices.
Serve the tomatoes immediately with the remoulade sauce.