Gail Simmons' Epic Spaghetti Pie

Name: Gail Simmons' Epic Spaghetti Pie
Prep time: 20 min
Cook time: 70 min
Total time: 90 min
Yield: 8 to 10
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