Crack the eggs into a small bowl, add the salt and black pepper, and beat thoroughly with a fork until smooth.

Melt half the butter in a non-stick skillet over medium heat and sauté the diced bell pepper, onion, and spinach for 3 to 4 minutes until tender. Transfer vegetables to a plate.

Melt the remaining butter in the same skillet, then pour in the beaten eggs so they spread evenly across the pan.

As the eggs begin to set, spoon the cooked vegetables and shredded cheese over one half of the omelet.

Carefully fold the other half of the omelet over the filling using a spatula, cook for another minute until the cheese melts, and serve warm.