Ingreadient

• 1 pound breakfast or italian sausage, removed from casing
• 4 tablespoons salted butter, at room temperature
• 14 to 16 slices (1/2-inch thick) french/italian bread, left out overnight or toasted
• 12 ounces gruyere, shredded
• 2 cups half-and-half
• 12 large eggs
• 1 tablespoon kosher salt
• cracked black pepper
• 3 cups broccoli florets with about 1 1/2 inches of stalk remaining
• 1 cup grated parmesan