In a mixing bowl, whisk together the eggs, milk or cream, salt, and black pepper until well combined and slightly frothy.
If using canned crab meat, drain it thoroughly. Gently flake the crab meat into bite-sized pieces, ensuring there are no shell fragments.
Heat the butter or oil in a non-stick skillet over medium heat until melted and bubbling.
Pour the egg mixture into the skillet, tilting the pan to spread it evenly across the surface. Allow the eggs to cook undisturbed for about 1-2 minutes, or until the edges begin to set.
Evenly distribute the crab meat over one half of the omelet. If desired, sprinkle chopped green onions, parsley, or chives over the crab meat for added flavor.
Using a spatula, carefully fold the unfilled half of the omelet over the crab-filled half to create a semicircle.
Continue to cook for an additional 1-2 minutes, or until the eggs are fully set and the crab meat is warmed through.
Gently slide the omelet onto a serving plate. Garnish with additional herbs if desired and serve immediately.
Notes
For extra flavor, try adding a dash of hot sauce or a squeeze of lemon juice to the crab meat before adding it to the omelet. You can also incorporate other ingredients like sautéed mushrooms, diced bell peppers, or shredded cheese.