Crack the eggs into a mixing bowl and beat them well.
Heat a heavy-bottomed 8 inch nonstick sauté pan over medium-low heat. Add the oil and heat.
Add milk and creole seasoning to the eggs. Whisk the eggs. Whisk and whisk like crazy. I’m just kidding, I just wanted to make you smile.
Saute or steam asparagus. Remove from heat, allow to cool and chop about 1/4 cup for the omelette.
Pour beaten eggs into the pan and cook for a couple of minutes. With a heat-resistant rubber spatula, gently push one edge of the egg into the center of the pan, while tilting the pan to allow the still liquid egg to flow in underneath. Repeat with the other edges, until there’s no liquid left.
Your eggs should now resemble a bright yellow pancake, which should easily slide around on the nonstick surface.
Now gently flip the egg pancake over, using your spatula to ease it over if necessary. Cook for another few seconds, or until there is no uncooked egg left.
Distribute crabmeat, chopped asparagus and Swiss cheese on one half of the omelette. With your spatula, lift one edge of the omelette and fold it across and over.
Gently transfer the finished omelette to a plate. Garnish with chopped fresh herbs if desired.