Cut each bread slice about 3/4 of the way through lengthwise, creating two connected slices. Spread 1/2 Tbsp. mustard on one interior cut side of each slice. Arrange cheese, tearing into smaller pieces if necessary, and a few slices of tomato inside each pocket of bread.
In a large, shallow baking dish, whisk together eggs, milk, salt and pepper. Add stuffed bread slices to egg mixture and let stand for 2 minutes. Flip and let stand 1 minute longer.
While bread is soaking, melt butter in a large skillet over medium heat. Add stuffed bread slices and cook until bread is golden and cheese has melted, 5 to 7 minutes per side, reducing heat if toast is browning too quickly.