Wake and Bake Breakfast Strata

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1 tablespoon unsalted butter, for the baking dish

14 to 16 ounces pretzel buns (about 4), cut into 1 1/2- to 2-inch cubes

9 large eggs

Kosher salt and freshly ground pepper

3 cups half-and-half

1 7-ounce can pickled sliced jalapeños, drained

8 ounces honey ham steak, cut into 1/2-inch cubes

6 ounces aged extra-sharp cheddar cheese, shredded off the block

6 ounces whole-milk mozzarella cheese, shredded off the block