In a large skillet over medium heat, melt the butter. Add in the onions and mushrooms and saute until both are golden, about 7-10 minutes.
Add the garlic and saute a minute more. Remove from heat and set aside.
Using a large snowflake-shaped cookie cutter, punch out snowflakes in the bread slices. Roughly tear all the leftover bread scraps and place in the bottom of a buttered 9 x 13-inch baking pan.
Layer over half the onion and mushroom mixture, spreading into an even layer.
Sprinkle over half the fontina cheese.
Add the snowflake-shaped bread in an even layer.
Add the remaining onion and mushrooms.
Sprinkle over the remaining fontina.
Whisk together the eggs, milk, oregano, salt and pepper and pour over the top of the bread. Top with parmesan cheese.
Refrigerate at least 8 hours or overnight.
Bake at 325°F for about 50-60 minutes, until golden-brown on top and no liquid egg mixture remains.