Preheat oven to 400°F. Grease a 9x13-inch baking dish.
Arrange tater tots in a single layer in the dish. Bake 20 minutes until starting to brown.
While tots bake, heat oil in a skillet. Sauté onion 4 minutes, add mushrooms and cook 5 minutes. Stir in spinach until wilted; cool slightly.
Whisk eggs, milk, salt, and pepper in a bowl. Stir in the veggie mix and half the cheese.
Pour egg mixture over partially baked tots. Sprinkle remaining cheese on top.
Bake 20–25 minutes until eggs set and top is golden. Let sit 5 minutes before cutting.