Scrambled eggs in French are creamy soft curds that just hold their shape from fork to mouth. Their preparation is entirely a matter of stirring the eggs over gentle heat until they slowly thicken as a mass into a custard. Salt plus half a teaspoon of liquid per egg helps blend yolks and white, but no more liquid or liquid-producing ingredients or the eggs will turn watery.
Beat the eggs in the bowl with the seasonings and liquid for 20 to 30 seconds, just to blend yolks and whites.
Smear the bottom and sides of the pan with the butter. Pour in the eggs and set over moderately low heat. Stir slowly and continually, reaching all over the bottom of the pan. Nothing will seem to happen for 2 to 3 minutes as the eggs gradually heat. Suddenly they will begin to thicken into a custard. Stir rapidly, moving pan on and off heat, until the eggs have almost thickened to the consistency you wish. Then remove from heat, as they will continue to thicken slightly.
Just as soon as they are of the right consistency, stir in the enrichment butter or cream, which will stop the cooking. Season to taste, turn out onto the platter, decorate with parsley, and serve.
(*) The eggs may be kept for a while in their saucepan over tepid water, but the sooner they are served the better.