Sauté onions in 1/4 cup butter. Crush the Ritz crackers and mix with the other 1/4 cup melted butter. Spread 3/4ths of the cracker crumbs in 9 x 13 dish. Layer onions on top. Salt and pepper to taste. Layer cheddar on top of onions. Mix together the eggs and milk, pour over cheddar. Sprinkle remaining cracker crumbs over top.
Bake 350º F for 35 to 40 minutes.