Melt the butter in a 3-quart saucepan over medium heat. Add the shallots and cook, stirring occasionally until tender, about 3-4 minutes.
Add the cognac and boil gently until the cognac is reduced by half. Add the stock and thyme, increase heat and bring to a boil, then reduce heat and simmer uncovered until reduced to about 1 cup, about 15-20 minutes.
Stir in the cream and black pepper and bring to a gentle boil. Simmer, stirring occasionally, until the sauce is reduced to about 2 cups and is a bit thicker than heavy cream, about 20 minutes.
Remove from heat. Stir in parmigiano, mustard , Worcestershire and lemon juice. Once cheese has melted, taste and add salt and/or more pepper as needed.