Season each tomato slice with sugar, salt, and pepper.

Beat milk and eggs together in a bowl. Pour flour into another bowl.

Gently press each tomato slice into flour to coat; shake off excess flour. Dip tomato slices into egg mixture, then press again into flour. Place breaded tomato slices onto a plate while breading the rest; do not stack.

Melt 1/2 cup butter in a large pan over medium heat. Place tomato slices in melted butter and cook until golden brown on one side, 5 to 7 minutes. Flip and cook on the other side until golden brown. Add more butter as need while frying.