Marinate the chicken breast in buttermilk for at least 1 hour.
In a bowl, mix flour, 1/2 teaspoon salt, and black pepper.
Remove chicken from buttermilk, dip in flour mixture, then in beaten egg, and again in flour mixture.
Heat vegetable oil in a skillet over medium heat.
Fry chicken until golden brown and cooked through, about 4-5 minutes each side.
Drain on paper towels to remove excess oil.
Assemble the sandwich by spreading mayonnaise on the toasted bun, adding lettuce, tomato slices, and the fried chicken breast.
Serve hot and enjoy.