Lightly butter 9x13-inch baking dish. Butter bread slices on both sides and line bottom of baking dish with 8 slices of bread. Saute scallions and ham cubes in butter until scallions are soft and ham is slightly browned. Distribute half the scallions and ham over bread slices. Top with half the cheddar and provolone cheeses. Repeat with buttered bread slices and ham and scallions. (Hold the cheese). Combine eggs and milk and pour over strata. Top with remaining cheese. Cover and refrigerate overnight.
In the morning: Bake in 350 degrees F oven, 30 minutes covered, 30 minutes uncovered, until strata is golden brown and puffy.