01 - In a mixing bowl, whisk together the eggs, milk, salt, and black pepper until well combined and slightly frothy.
02 - Heat a non-stick skillet over medium heat. Add the chopped red onion, bell pepper, and jalapeño; sauté for 2 to 3 minutes until softened. Stir in the diced tomato and black beans, cooking for another minute. Transfer the vegetable mixture to a bowl and wipe the pan clean.
03 - Lightly coat the skillet with oil or butter. Pour in the egg mixture, swirling the pan to evenly coat the surface. Cook undisturbed for 1 to 2 minutes until the bottom is mostly set.
04 - Spread the sautéed vegetables evenly over one half of the omelette. Top with shredded cheese and half of the chopped cilantro.
05 - Using a spatula, gently fold the omelette in half to enclose the filling. Continue cooking for 1 to 2 minutes until the cheese is fully melted and the eggs are cooked through.
06 - Slide the omelette onto a plate. Garnish with the remaining cilantro, avocado slices, salsa, and lime wedges. Serve immediately.