Prepare the Crab Meat: If using fresh crab, clean and flake the crab meat into small pieces. If using canned or imitation crab, drain and flake it as well. Set aside.
Whisk the Eggs: Crack the eggs into a bowl, season with salt and pepper, and whisk until smooth. Optionally, add a splash of milk or cream for a fluffier omelette.
Heat the Pan: Place a non-stick frying pan over medium heat. Add the olive oil or butter and swirl it to coat the bottom of the pan.
Cook the Omelette: Pour the whisked eggs into the pan and let them cook for 1-2 minutes until the edges set, but the center is still slightly runny.
Add the Crab Meat: Sprinkle the flaked crab meat over one half of the omelette. If desired, add grated cheese over the crab for extra creaminess.
Fold and Finish Cooking: Gently fold the omelette in half using a spatula. Let it cook for another 1-2 minutes until fully set but still moist inside.
Garnish and Serve: Garnish with fresh herbs, a squeeze of lemon juice, or a dash of hot sauce if desired. Serve hot with toast or a side salad.