Heat oil in a medium nonstick pan. Add tortilla pieces and cook, flipping once, until crispy, about 3 minutes. Add spinach and cook, stirring, until wilted, about 1 minute. Lightly beat eggs in a small bowl and season with salt and pepper; add to the pan. Cook, stirring, until set, about 2 minutes. Stir in cheese and remove from heat. Top with avocado.