In a large mixing bowl, crack the eggs and whisk them until well beaten. Season with salt and pepper to taste.
Heat the butter or cooking oil in a large skillet or frying pan over medium heat.
Add the diced bell peppers and onions to the skillet and sauté for 2-3 minutes, or until they begin to soften.
Add the diced tomatoes and cooked crab meat to the skillet and cook for an additional 2 minutes, stirring occasionally.
Pour the beaten eggs into the skillet, making sure they cover the entire surface evenly.
Allow the eggs to cook undisturbed for 2-3 minutes, or until the edges begin to set.
Using a spatula, gently lift the edges of the omelet and tilt the skillet to allow the uncooked eggs to flow underneath.
Once the omelet is mostly set but still slightly runny on top, sprinkle the shredded cheddar cheese evenly over the surface.
Carefully fold the omelet in half using the spatula and cook for an additional 1-2 minutes, or until the cheese is melted and the eggs are cooked through.
Slide the omelet onto a serving platter and garnish with chopped fresh parsley.
Slice the omelet into portions and serve hot.
