Preheat oven to 375 degrees F.
Cut twelve 1/2-inch thick slices from tomatoes. In a shallow bowl whisk together flour, salt, sugar, and cayenne. In another shallow bowl whisk together egg and milk. In a third shallow bowl coarsely crush cornflakes with hands.
Working with 1 tomato slice at a time, dredge in flour, shaking off excess, and dip in egg, letting excess drip off. Coat slices with cornflakes, pressing them to adhere, and arrange slices in one layer on a baking sheet.
In a 12-inch nonstick skillet heat 1 tablespoon butter and 1 tablespoon oil over moderate heat until foam subsides and fry 3 tomato slices until golden brown, about 3 minutes on each side. (Be careful not to let cornflakes burn.) Transfer tomatoes to paper towels to drain. Fry remaining tomato slices in remaining butter and oil in same manner. On another baking sheet arrange drained tomato slices in one layer. Bake tomatoes in middle of oven until tender and hot, about 4 minutes.
Serve tomatoes topped with salsa.
Quarter and seed tomatoes. Cut tomatoes into 1/4-inch dice and transfer to a bowl. Wearing rubber gloves, seed and finely chop chiles. Finely chop enough onion to measure 1/4 cup and chop cilantro. Stir chiles, onion, cilantro, and garlic into tomatoes with sugar and lime juice and salt and pepper to taste. Salsa may be made 1 hour ahead and kept at cool temperature.