Put hot sauce in small dish for dipping. Mix flour, brown sugar, grill seasoning, salt, and pepper in a separate small dish. Beat eggs into milk in a third dish. Pour panko in a fourth shallow dish. Arrange dishes in a line, respectively.
Dip one side of each tomato slice in hot sauce. Press each side of tomato into flour mixture to coat; dip into milk mixture. Gently press tomato slices into panko to coat. Arrange coated tomatoes on a baking sheet. Refrigerate until chilled, about 30 minutes.
Heat oil in a deep-fryer or a cast-iron skillet to 375 degrees F (190 degrees C).
Fry tomato slices in hot oil until golden brown, 2 to 3 minutes per side.
