In a deep bowl, mix the buttermilk (sour milk) with the egg white, beat with a whisk or fork until smooth. In another bowl, combine all the flour and ground black pepper.
Take the tomato slices one at a time and dip them first in buttermilk and then in flour.
Heat a large skillet over medium heat, brush with oil. Place the tomatoes in a preheated pan and cook for about 3 minutes on each side. Transfer the tomatoes to a paper towel.
Fry the bacon strips until crisp, cut in half.
Cut the buns in half. Grease the slices of the halves with 1 teaspoon of mayonnaise. On the base halves, put 1 lettuce and 2 slices of tomato. Put 2 halves of bacon on the tomatoes. Cover with a half-top bun.