In a bowl, whisk eggs with salt and pepper. Set aside.
Heat 1 teaspoon coconut oil over medium-high heat in a sauté or frying pan that has a lid. Add garlic, spinach, peppers, onion, tomato, and mushroom. Sauté until veggies are soft, about 3−5 minutes. Remove vegetables from pan. Set aside in a bowl.
Heat the remaining 1 teaspoon coconut oil in the pan. Pour the eggs in the pan evenly. Add in the veggies on top of the egg mixture, reduce heat to low, cover pan with lid. Cook for about 2 minutes. If the egg is still uncooked, cook for another minute uncovered. Fold the omelet in half.