4 cups day-old or toasted cubed pumpernickel bread, divided
2 cups day-old or toasted cubed sourdough bread, divided
8 ounces sliced black forest deli ham
2 cups grated Gruyère cheese, divided
12 large eggs
2 1/2 cups whole milk
1/4 cup whole-grain mustard
1 teaspoon kosher salt
1/4 teaspoon freshly ground black pepper
Coat a 9x13-inch baking dish with cooking spray.
Place half of the pumpernickel and half of the sourdough bread cubes in an even layer in the baking dish. Place the slices of ham evenly over the bread cubes, then sprinkle with half of the cheese. Evenly top with the remaining pumpernickel and sourdough bread cubes, then sprinkle with the remaining cheese.
Whisk the eggs, milk, mustard, salt, and pepper together in a large bowl. Pour the egg mixture evenly over the casserole. Cover with plastic wrap or aluminum foil and refrigerator overnight.
Arrange a rack in the middle of the oven and heat to 350°F. Remove the casserole from the refrigerator and let it sit at room temperature while the oven heats.
Uncover and bake until the eggs are set, puffed, and golden brown, 50 to 55 minutes. Let cool for 5 minutes before slicing and serving hot.