Special equipment: 9-inch nonstick springform pan
Preheat the oven to 375 degrees F. Bring a large pot of generously salted water to a boil. Cook the pasta until still slightly crunchy and undercooked, about 2 minutes. Drain and set aside.
Wipe out the pot, add the oil and heat over medium-high heat. Add the sausage, onions and garlic and cook, flipping the sausage and stirring occasionally, until the sausage is browned and the onions are soft and starting to brown, about 8 minutes. Stir in the tomato paste and cook until fragrant, about 1 minute. Add the crushed tomatoes, 1/2 cup water, 2 teaspoons salt and a few grinds of pepper and bring to a boil. Reduce to a simmer, cover and cook until the sauce starts to thicken and the sausage is cooked through, about 25 minutes. Remove the sausage from the pan and set aside. Add the pasta to the pan and stir to coat.
Meanwhile, coat a 9-inch nonstick springform pan with cooking spray. Roll out 1 puff pastry sheet to a 13-inch square. Transfer it to the prepared pan, pressing it into the bottom and up the sides and allowing the excess pastry to hang over the rim. Spread half of the pasta mixture in the pan. Arrange the sausage on top of the pasta around the rim of the pan to create a ring. Evenly spread the spinach in the middle of the sausage ring. Top with the mozzarella, then the rest of the pasta mixture. Place the second pastry sheet on top of the pasta and pinch the edges of both the bottom and top pastry together to seal, then trim the edges. Cut a slit in the center of the puff pastry to allow the steam to escape.
Bake until the pastry is browned and puffed on top, about 1 hour and 30 minutes. Let cool for 30 minutes before serving. Remove the pan and cut into wedges.
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