Heat a large Dutch over medium-high heat. Add enough olive oil to lightly coat the bottom of the pan. Add the sausage and cook just until well browned on all sides, about 5 minutes. Add the onions, garlic, celery, and carrots and cook until the vegetables begin to soften, about 8 minutes. Season with salt and pepper and add the crushed red pepper flakes. Add the fresh tomato puree and the red wine and bring to a simmer. Lower the heat and simmer gently for 30 minutes. Season, to taste, with salt and pepper.
Bring a large pasta pot of water to a boil. Season with salt. Add the rigatoni and cook according to package directions, or until al dente, about 8 minutes. Drain well.
Place the portobello mushrooms on the bottom of a large platter. Top with the drained pasta. Pour the ragout over the pasta. Shave curls of the pecorino over the pasta with a vegetable peeler.
Preheat a grill or a grill pan.
Drizzle both sides of the mushrooms with olive oil and season with salt and pepper. Place on the grill and grill until tender, about 4 minutes per side.
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