Preheat oven to 400 degrees F (200 degrees C). Grease a 9x13-inch baking dish.
Bring chicken broth to a boil in a pot; stir in orzo. Cook until almost tender, about 7 minutes. Pour orzo and broth into a bowl.
Heat butter in a skillet over medium heat; cook and stir onion and mushrooms in the melted butter until softened, about 7 minutes. Pour in Marsala wine and simmer until liquid is reduced by half, 5 to 10 minutes. Stir mushroom mixture into orzo.
Stir peas, cream, fontina cheese, mozzarella cheese, salt, and pepper into orzo-mushroom mixture. Transfer to the prepared baking dish.
Mix bread crumbs, Parmesan cheese, and thyme together in a bowl; sprinkle over orzo-mushroom mixture.
Bake in the preheated oven until cheese is melted and breadcrumbs are lightly browned, about 25 minutes.