Begin by chopping the red onion, red bell pepper, jalapeño, and tomato into small pieces. Rinse and drain the canned black beans in a colander.

In a non-stick skillet, heat a splash of olive oil over medium heat for about 1 minute. Add the chopped onion and bell pepper, sautéing them until softened and slightly translucent, around 3–4 minutes. Stir in the jalapeño and tomato, cooking for an additional 2 minutes.

In a mixing bowl, whisk together the eggs with a splash of whole milk, seasoning with salt and black pepper until well combined and slightly frothy.

Return the skillet to the stove and lower the heat to medium-low. Add butter or oil, and pour in the egg mixture, cooking for 3–4 minutes until edges are set yet the center remains slightly runny.

Once the omelette's edges begin to set, spoon the sautéed filling and shredded cheese across one half. Carefully fold the other half over the filling and cook for another minute until the cheese melts.

Gently slide the omelette onto a plate. Top with sliced avocado, cilantro, salsa, and lime wedges before serving.