In a saucepan, saute the onion, mushrooms and thyme in 4 tablespoons of the butter until mushrooms wilt. Add wine and continue to simmer for 10 more minutes.

Use the remaining butter to grease a medium-size baking dish. Start with a layer of bread, then sprinkle cheese followed by onion/mushroom mixture. Repeat until you have three layers, ending with a layer of bread.

Beat together the eggs, milk, salt and pepper and pour over layered strata. Cover and refrigerate for at least 2 hours or overnight (preferred).

Bake in a preheated 350 degree oven for 20-30 minutes or until golden brown on top.