unsalted butter (for greasing the pan)
2 tablespoons extra-virgin olive oil
1 medium yellow onion (finely chopped)
2 cloves garlic (peeled, finely chopped)
1/4 pound broccoli or broccoli rabe (trimmed, stems and florets chopped into 1/4-inch thick pieces – about 2 1/2 cups)
1 pound hot or sweet Italian sausage (removed from casings)
1 tablespoon tomato paste
1 28- ounce can whole peeled tomatoes (drained, crushed by hand)
Kosher salt (to taste)
1 pound dried spaghetti
3/4 cup whole milk
3 large eggs
2 teaspoons freshly ground black pepper
2 1/2 cups sharp yellow cheddar cheese (grated, 8-ounces)
2 1/2 cups fontina cheese (grated, 8-ounces)
1 1/2 cups Parmigiano-Reggiano cheese (freshly grated, 3-ounces, divided)
1 tablespoon fresh sage (finely chopped)

Bring a large pot of salted water to a boil. Heat the oven to 425ºF. Butter a 9 and 1/2-inch spring-form pan. Tightly wrap the bottom of the pan with a large sheet of foil, crimping the foil against the outer edges to tightly seal.
In a large skillet, heat the oil over medium-high heat. Add the onion and garlic and cook for 1 minute. Add the broccoli and 1 tablespoon water and cook until the broccoli is crisp-tender, 2 to 3 minutes. Add the sausage and cook, breaking the meat into small bits, until cooked through, about 6 minutes. Stir in the tomato paste and cook 1 minute, then add the crushed drained tomatoes and 1/4 teaspoon salt. Cook, stirring occasionally and scraping any bits from the pan, until the liquid is mostly evaporated, about 5 minutes. Remove from the heat and set aside.
Add salt to the boiling water and cook the spaghetti just until very al dente, 7 to 8 minutes (look for a white spot in the center when you bite into a strand). Drain the pasta (do not rinse) and reserve the pot.
In the pasta pot, whisk together the milk, eggs, pepper, and 3/4 teaspoons of salt. Stir in the cheddar, fontina, and 1 cup of the Parmesan. Add the sausage mixture and spaghetti; stir until well combined.
Transfer the pasta mixture to the prepared pan. Using a spatula, smooth the top. Set the pan on a rimmed baking sheet and bake until the edges are golden and bubbling, about 35 minutes.
Remove the pan from the oven. Turn on the broiler. Sprinkle the pie with the sage and remaining 1/2 cup Parmesan. Broil 4 to 5 inches from the heat until the cheese is golden, 2 to 3 minutes. Remove from the oven and run a knife around the inside of the pan. Let the pie rest about 10 minutes then release and remove the sides of the pan. Cut the pie into slices and serve warm.
Tip: Get creative! Substitute your favorite protein and vegetable to give this spaghetti pie your own personal flair!