Step 1: Bring a large pot of salted water to a boil. Add the pasta and cook as the label directs for al dente, about 12 minutes.
Step 2: Reserve 3/4 cup cooking water, then drain.
Step 3: Meanwhile, melt the butter in a large skillet over medium-high heat. Add the onion, carrots, garlic, 1/4 teaspoon salt and a few grinds of pepper. Cook stirring occasionally, until softened, 6 to 8 minutes.
Step 4: Add the ground beef, 1/4 teaspoon salt and a few grinds of pepper and cook, breaking up the meat, until no longer pink, about 4 minutes.
Step 5: Add the tomato paste and cook until evenly combined 1 minute.
Step 6: Add the wine and simmer until almost completely dry, 1 to 2 minutes. Add 1/2 cup of the reserved cooking water, the tomatoes and half the basil. Bring to a boil, then reduce the heat to a simmer and cook until the tomatoes start to burst and the mixture is saucy, 4 to 7 minutes.
Step 7: Add the cheese to the sauce, then add the rigatoni; season with salt and pepper and toss, adding more cooking water as needed to loosen.
Step 8: Divide among bowls and top with the remaining basil and more Parmesan.
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