Everything Bagel Breakfast Casserole

Ingredients (10)

• 6 leftover everything bagels halved horizontally and cut or torn into bite-sized pieces (see notes if your bagels are fresh or very soft)
• 6 ounces cooked ham bacon , or sausage, cut or crumbled into small pieces
• 3/4 cup freshly grated sharp cheddar cheese divided
• 8 large eggs
• 2 1/2 cups milk
• 1 teaspoon ground mustard
• 1/2 teaspoon kosher salt
• 1/4 teaspoon black pepper
• 2 tablespoons chopped fresh chives plus additional for sprinkling on top
• 8 ounces reduced-fat cream cheese or regular cream cheese; do not use fat free