Remove crusts from bread and butter one side of each slice. Lay 6 pieces, buttered side down, into a 9 X 13 greased baking dish. Place cheese over bread and stack ham over cheese. Cover with remaining 6 pieces of buttered bread, buttered side up.

Beat together the egg and milk and pour over the sandwiches.
Cover and refrigerate overnight.
Set out for 30 minutes and then bake at 325 for one hour.
While baking make up sauce.

Sauce:
1 cup sliced mushrooms
1 Tbs. butter
1 Tbs. flour
1 cup milk
salt & pepper to taste
1 tsp sherry (optional)
Sauté the mushrooms in the butter, remove from heat and add the flour to make a roux. Add the milk and cook, stirring, until thickened. Season with salt, pepper, and sherry. (if desired).