Foryoueats: Gail Simmons' Epic Spaghetti Pie

Ingredients

• Unsalted butter, for greasing the pan
• 2 tablespoons extra-virgin olive oil
• 1 medium yellow onion, finely chopped
• 2 cloves garlic, finely chopped
• ¾ lb broccoli or broccoli rabe, trimmed, stems and florets chopped into ¼-inch pieces (about 2 ½ cups)
• 1 lb hot or sweet Italian sausage, removed from casings
• 1 tablespoon tomato paste
• 1 (28-ounce) can whole peeled tomatoes, drained, tomatoes crushed by hand
• Kosher salt
• 1 lb dried spaghetti
• ¾ cup whole milk (I substituted half & half)
• 3 large eggs
• 2 teaspoons freshly ground black pepper
• 2½ cups (8 oz) grated sharp cheddar cheese
• 2½ cups (8 oz) grated fontina cheese
• 1½ cups (3 oz) freshly grated Parmigiano-Reggiano cheese, divided
• 1 tablespoon finely chopped fresh sage
• Special equipment: 9½-inch springform pan