Preheat oven to 350 degrees F (175 degrees C). Spray a 9x13-inch baking dish with cooking spray.

Layer Cheddar-Monterey Jack cheese blend and mozzarella cheese in the prepared baking dish.

Heat 2 tablespoons butter in a large skillet over medium-high heat; saute mushrooms and green onions until mushrooms are golden brown, 5 to 10 minutes. Add spinach and tomatoes; saute just until spinach wilts, 3 to 5 minutes. Spoon vegetable mixture over cheese mixture.

Whisk eggs, half-and-half, mustard, marjoram, tarragon, and black pepper together in a bowl; pour over vegetable mixture. Dot remaining butter on the egg mixture.

Bake in the preheated oven until a knife inserted near the center comes out clean, 35 to 45 minutes. Let stand 5 minutes before serving.