Truss the capon as if to be baked. Brown in butter in a casserole without burning the butter (at least 25 minutes). Sprinkle with the Cognac, flambÄ. Salt, pepper, add the whole onion and 1/2 glass of Champagne. Cook over a low heat for 1 1/2 hours. Take out the capon, keep warm. Skim the fat off the sauce. Gently fry the thinly sliced onions in 1 tablespoon butter without allowing to brown, moisten with 1 glass of champagne, bring to a boil, add the skimmed sauce. Dissolve the cornstarch in a little cold water, remove the sauce from the heat and add half of the dissolved cornstarch, thicken, add more if necessary. The sauce must be slightly thickened but not really thick. Put through a fine sieve. Make a dark caramel with the sugar and the vinegar, thin by adding a few drops of boiling water. Use to slightly color the sauce, boil. Adjust the seasoning. Remove the sauce from the heat, add 3 tablespoons melted butter, little by little, whisking. Serve the capon surrounded with grilled sausages, coated with a little sauce, serve the remaining sauce in a gravy boat. Serve with chestnuts cooked in butter over a low heat.