Beurre blanc, a renowned French sauce, breaks down easily and cannot be reheated. If it turns oily, beat a spoonful of it in a chilled bowl until creamy, then add the rest of the sauce a spoonful at a time.
After boiling down the shallot mixture and adding the whipping cream, boil the sauce gently for 2 to 3 minutes to thicken. Remove from the heat and whisk in the first piece of butter. Incorporate each piece of butter completely before adding the next.
As the butter is blended into the sauce mixture, the sauce becomes silken and smooth. Remember to incorporate each piece of butter completely before adding the next; this keeps the sauce at the right consistency. Season with pepper, strain to remove the shallots, then spoon over the chicken.