1. In a 10- to 12-inch ovenproof frying pan over high heat, stir butter and shallots often until shallots are lightly browned, about 3 minutes.
2. Add grain mix and stir until grains are lightly toasted, about 2 minutes. Add broth and marjoram, stir, and bring to a boil. Cover, reduce heat, and simmer until grains are tender to bite, about 12 minutes, stirring occasionally.
3. Mix 1/2 cup cheese with pilaf. Using the back of a spoon, make 4 deep wells in mixture. Slide 1 egg into each well. Lay tomato slices around eggs.
4. Bake in a 400° oven until egg whites are opaque and yolks have desired texture, about 8 minutes for liquid yolks. About 3 minutes before eggs are cooked, sprinkle mixture with remaining cheese.
5. Use a wide spatula to scoop out pilaf and eggs, 1 at a time, and put on plates. Add salt and pepper to taste.