Melt the butter in a saucepan and add the shallots.
Cook gently over low heat for about 2 minutes, until the shallots are soft but not brown.
Add the Madeira, bring the mixture to a boil and reduce it by half to concentrate the flavor.
Mix in the demiglace, return the mixture to a boil and add the dissolved potato starch and salt and pepper to taste.
Just before serving, add the chopped truffles and Cognac.
Bring the mixture to a boil, cover tightly to prevent the aroma from evaporating and serve as soon as possible with the truffled potatoes Sarladaise (see recipe) or with meat.