Generously salt tomato slices and let sit for 10 minutes on paper towels.
Meanwhile, whisk together sour cream, mayonnaise, lemon zest, lemon juice, white pepper, and chopped basil to create the sauce. Set aside.
In a shallow bowl, combine flour, cornmeal, black pepper, and Aleppo pepper.
In another shallow bowl, beat the egg with hot sauce.
Pat the tomato slices dry. Dredge each slice in the flour mixture, then dip in the egg mixture, and coat again with the flour mixture.
Heat about ½ inch of oil in a large skillet over medium heat. Fry the tomatoes until golden and crispy, about 2–3 minutes per side. Drain on paper towels.
Toast the sandwich rolls if desired. Spread the basil sour cream on the bottom half, top with fried tomatoes, a drizzle of chile oil, and extra basil. Close the sandwich and serve immediately.