Coat a 13x9x2-inch glass baking dish with cooking spray. From the party tray, set aside 2 ounces each pepperoni and salami and 3 ounces each cheddar and jack cheese; reserve the remaining meat and cheese for another use. Arrange the bread, 2 ounces pepperoni, 2 ounces salami, 3 ounces cheddar, and 3 ounces jack cheese in slightly overlapping layers in the dish, covering the whole dish.
In a large bowl, whisk together the eggs, milk, basil, and pepper. Pour over the bread mixture, cover tightly with plastic wrap, and refrigerate for at least 2 hours and up to overnight.
Preheat the oven to 375 Degrees F. Uncover the bread mixture and bake until set and a tester inserted in the center comes out clean, about 40 minutes.