1 (1-pound) day-old sourdough boule, cut into 1-inch cubes
4 large eggs
3 1/2 cups whole milk, or any combination of milk and cream
1/2 teaspoon ground nutmeg
1/2 teaspoon kosher salt
1/4 teaspoon freshly ground black pepper
Cooking spray or butter
1 cup caramelized onions
1 1/2 cups shredded provolone cheese, divided
8 ounces thick-cut ham, cut into 1/2-inch cubes
2 tablespoons thinly sliced fresh chives, for garnish