Butter, for greasing
2 tablespoons extra-virgin olive oil
1/2 cup finely diced pepperoni (2 ounces)
1/2 pound shiitake mushrooms, stems discarded and caps cut into 3/4-inch pieces
1 medium onion, minced
1 red bell pepper, cut into 1/2-inch pieces
2 teaspoons kosher salt, plus more for seasoning
8 large eggs
3 cups whole milk
1 tablespoon Dijon mustard
1 tablespoon soy sauce
1/2 teaspoon pepper
3/4 pound day-old challah, sliced 1 inch thick and cut into 1-inch dice (10 cups)
6 ounces Black Forest ham, finely diced (1 1/4 cups)
1 cup shredded Monterey Jack cheese (1/4 pound )
1 cup shredded aged white cheddar cheese (1/4 pound )
1/2 cup finely chopped scallions, plus thinly sliced scallions for garnish
Hot sauce, for serving

Butter a 9-by-13-inch baking dish. In a large skillet, heat the olive oil. Add the pepperoni and cook over moderate heat until the fat is rendered, about 3 minutes. Add the shiitake and cook until lightly browned and tender, about 5 minutes. Add the onion, bell pepper and a generous pinch of salt and cook, stirring occasionally, until softened and browned, about 7 minutes; let cool completely. In a large bowl, beat the eggs with the milk, mustard, soy sauce, pepper and 2 teaspoons of salt. Add the cooled vegetable mixture, challah, ham, both cheeses and the chopped scallions and mix well. Scrape the mixture into the prepared baking dish, cover with plastic wrap and refrigerate overnight. 
 Preheat the oven to 350°. Uncover the casserole and bake for about 50 minutes, until it’s just set and the top is browned. Let stand for 10 minutes, then top with thinly sliced scallions and serve with hot sauce.