Cut tomatoes into 1/8- to 1/4-in.-thick slices and lay on paper towels (to soak up some of their juices). Set aside.
In a medium bowl, whisk together eggs, milk, Dijon mustard, salt, thyme, pepper, and dry mustard. Soak each bread slice in egg mixture for about 30 seconds.
Heat oil in a large pan over medium-high heat. Working in batches of 4 slices, cook bread until browned on one side, 1 minute. Turn bread over and top with 1 slice tomato and 1 slice cheese. Reduce heat to low, cover pan, and cook until cheese melts, about 2 minutes. Serve hot.