1. Make the remoulade sauce. Whisk all of the sauce ingredients together in a small bowl until combined. Cover and refrigerate until ready to serve.
2. Season the flour. Stir 1/3 cup of the flour, salt, and paprika together in a wide, shallow bowl or pie plate.
3. Make the wet mixture. Whisk the buttermilk, egg white, and hot sauce together in second wide, shallow bowl.
4. Prepare the cornmeal. Stir the cornmeal and remaining 1/3 cup flour together in a third wide, shallow bowl.
5. Bread the tomato slices. Fit a wire rack inside a rimmed baking sheet. Dip each tomato slice in the flour mixture, followed by the buttermilk mixture, and finally the cornmeal mixture.
6. Set the cornmeal coating. Place the breaded tomato slices on the rack in a single layer. Let sit so the coating sets while the oil heats.
7. Heat the oil. Heat the oil in a large cast iron skillet over medium-high heat until shimmering, about 5 minutes. The oil should sizzle immediately if you sprinkle flour into it.
8. Fry the tomatoes. Carefully add 4 to 5 tomato slices and fry until golden-brown, 3 to 5 minutes per side. Transer the fried tomatoes to a paper towel-lined plate. Fry the remaining tomato slices.
9. Serve warm the remoulade sauce. Serve the tomatoes immediately with the remoulade sauce.

Make ahead: The remoulade sauce can be made up to 2 days in advance. Fried tomatoes are best eaten immediately after frying.

Storage: Refrigerate leftover remoulade sauce in an airtight container for up to 2 days.