In a small sauté pan, sauté diced shallots in butter over medium heat until soft.
Add thyme and champagne, and as the mixture simmers, slowly whisk in the cornstarch. Add the Blue Brie and continue to whisk until cheese is melted and creamy. Incorporate 3 ounces of the grated Manchego. If fondue is too thick, add a splash of champagne. If it is too thin, add more Manchego and a pinch of cornstarch. Salt and pepper to taste.