Pulse the onions, carrots, and garlic in a food processor until they resemble small pebbles. Set aside.

Heat a large Dutch oven over high heat. Add 2 tablespoons olive oil, then the beef, veal, and sausage. Cook, breaking up the meat, until the moisture evaporates and the meat is deeply browned, about 20 minutes. The meat should be very finely broken up. Season with 1 teaspoon fine sea salt and plenty of freshly cracked black pepper. Transfer to a plate, leaving the fat in the pan. If there is excessive fond, deglaze with a splash of stock or water and pour the excess over the meat.

Add the remaining 2 tablespoons olive oil to the Dutch oven. Add the vegetables and cook, stirring, until softened, 6 to 8 minutes. Season with 1 teaspoon fine sea salt and pepper. Return the meat and juices to the pot. Stir in the tomato paste and cook, stirring, until brick red, about 10 minutes.

Add the wine and cook until reduced by half, 3 to 4 minutes. Tie the thyme and rosemary together with kitchen twine and add to the pot along with the stock, tomatoes, cheese rinds, and 1 teaspoon fine sea salt.

Cover and simmer over medium-low heat until thickened, about 1½ hours. Season with the remaining 1 teaspoon salt and freshly cracked black pepper.

About 20 minutes before serving, bring a large pot of salted water to a boil. Add the pasta and cook as the label directs. Strain off the water (reserving 1 cup) and add some of the sauce to the same pot you cooked the pasta in. Add a bit of parmesan cheese, olive oil, and pasta water and toss to emulsify the sauce.

Plate and finish with more Parmesan and torn fresh basil. Refrigerate the leftover sauce for up to 3 days or freeze up to 1 month.