Heat oven to 400 degrees F. Arrange the tots on a rimmed baking sheet and bake for 20 minutes. Meanwhile, heat the oil in a large ovenproof skillet over medium heat. Add the onion, season with 1/2 teaspoon each salt and pepper, cover and cook, stirring occasionally, for 5 minutes. Add the red pepper and mushrooms and cook, stirring occasionally, until the vegetables are just tender, 5 to 6 minutes. Toss with the garlic and tomatoes and cook for 1 minute. Fold in the spinach and tots. Make 8 small wells in the vegetable mixture and carefully crack an egg into each. Sprinkle with the cheese and bake the eggs to desired doneness, 15 to 18 minutes for slightly runny yolks.