Combine the crabmeat, shallots, and green onions in a small mixing bowl. Season with salt and pepper.
In a stainless steel bowl set over a pot of simmering water (be careful not to let the bowl touch the water), whisk the yolks with the lemon juice, Tabasco, and water until pale yellow in color. Season with salt and pepper. Remove the bowl from the pot and, whisking vigorously, add the melted butter, 1 tablespoon at a time, until all the butter is incorporated. Add the tasso and continue whisking for 30 seconds. Keep warm.
In a large mixing bowl, whisk the eggs and heavy cream together and season with salt and pepper.
In a 6-inch nonstick sauté pan over medium heat, heat 2 tablespoons of the butter until it foams. Pour in one-fourth of the egg-cream mixture and cook, shaking the pan and stirring rapidly with a fork, holding the tines parallel to the bottom of the pan. The omelet should remain runny in the center but firm on the bottom.
Lift the handle of the skillet and gently knock the pan on the surface of the stove so the omelet slides to the bottom curve of the pan. Add 1/4 cup of the crab mixture and 1/4 cup of the grated cheese in the center of the omelet, then, with a fork, quickly fold the omelet from the top down. Let it stand for a few moments, then slide it onto a serving plate. Repeat the process until all the egg mixture and butter are used.
To serve, spoon the sauce over each omelet and garnish with green onions.
Yield: 4 servings