Pour milk into shallow dish. Place flour in separate shallow dish. In third dish, lightly beat eggs.
Dip both sides of bread into milk to moisten but not soak. Place cheese on 2 of the slices; spread with mustard. Top with tomato; sprinkle with pepper. Top with remaining bread. Holding sandwiches together, dip into flour then eggs to coat.
In nonstick skillet, heat oil over medium heat; cook sandwiches, pressing slightly occasionally and turning once, until crisp and golden and cheese is melted, about 8 minutes.