Saut in a skillet or fry pan, the onion and broccoli, in olive oil.
Cook until just slightly soft (onion) and broccoli is still firm and bright green. Lightly butter a 9 x13 inch baking pan. Lightly butter bread slices. Line bottom of pan with bread slices. Cover with onion, broccoli and cheese. In a mixing bowl, mix eggs, milk, paprika, salt and pepper.
Pour egg mixture into pan, and let set and soak up eggs overnight in the refrigerator, (or bake immediately). If baking immediately: Preheat oven to 325. Bake about 1 hour, until eggs are set/solid.