Dice the onion, carrot, and celery (you can do this quickly in a food processor). Dice garlic, measure out seasonings, and set out the rest of the ingredients.
Bring a large pot of water to boil and generously salt the water. Set a large colander in the sink with a glass mug in the center (so you don’t forget to grab some pasta water before draining). Once salted water is boiling, add rigatoni (not the whole box, just 3-1/4 cups!) and cook according to package directions, draining pasta 1 minute before directed. Before draining, pull out a mugful of water, then drain. Do not rinse.
Meanwhile, add the olive oil to a large, heavy-bottomed pot or Dutch oven; heat to medium-high. Add carrot, onion, and celery. Season to taste. (I add 1/4 teaspoon salt and pepper.) Cook, stirring occasionally, until becoming soft, about 5–7 minutes. Add sausage and cook, crumbling as you go, until browned through. Add garlic, seasonings, and tomato paste. Season to taste with salt and pepper. (I add 1/4 teaspoon each again.) Cook, stirring constantly, until very fragrant and tomato paste begins to darken, about 3–5 minutes. Reduce heat if anything is burning.
Add vinegar and stir until evaporated. Add chicken broth—it should sizzle and boil. Cook until mostly all is evaporated. Reduce heat to low and add cream. Mix and allow sauce to come to a low simmer. Cook until slightly thickened, about 3 more minutes.
Add coarsely chopped spinach and pasta. Use tongs to vigorously toss the sauce with the cooked pasta. If needed, slowly add the reserved pasta water to thin the sauce until the sauce clings nicely to the pasta. Taste and season if needed with additional salt. Serve with a generous sprinkle of Parmesan, red pepper flakes if desired (for some heat!), and fresh herbs, if using.
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Notes
Note 1: Mirepoix: Save time by dicing veggies in a food processor, or use pre-made mirepoix (sometimes called soup starter). Most stores sell pre-chopped mirepoix in the produce section. You can even use frozen mirepoix–found near other frozen veggies in the store.Note 2: Sausage can come in different-sized packages—as long as you’re close to 1 pound, this recipe will work fine. If using sausages with casings, remove the casings before cooking. If sausage doesn't leave behind 2 tablespoons grease, add 2 tablespoons olive oil.Note 3: For a stronger fennel flavor, use up to 2 teaspoons. Measure and crush the seeds (mortar and pestle or pound in a bag with the bottom of a frying pan) and add in. Ground fennel is stronger, so you’ll need less. You may want to increase other seasonings a bit if you can’t find fennel.Note 4: Vinegar adds nice acidity when paired with chicken broth. If you’d like to use wine instead, leave out the vinegar and replace 1/2 cup chicken broth with a white wine like a Chardonnay or Sauvignon blanc. Be sure to cook it off like the chicken broth is cooked off. (You’ll still add the other 1/2 cup chicken broth after adding the wine.)Note 5: Optional Toppings: Parmesan cheese, fresh herbs (like thyme, parsley, or basil), and red pepper flakes.Storage: This dish is best enjoyed right after cooking. You can store leftovers but may need extra chicken stock when reheating. Avoid freezing; the pasta can get mushy.