Heat 2 tbsp of olive oil in a large, deep skillet over medium heat. Add your finely minced onion, carrot, and celery. Cook until the veggies are soft and the onions are translucent.
Clear a small space in the center of your veggies. Drop in 2 tbsp of tomato paste and let it fry directly on the bottom of the pan for 1 minutes until it shifts to a dark brick-red, then stir it into the vegetables.
Pour in the canned crushed tomatoes. Add a small pinch of salt and black pepper. Bring to a gentle bubble, turn the heat to medium-low, and let it simmer and thicken while you boil your pasta. Add pasta water if required.
Roughly shred your carbonnade beef and stir it into the pan while atill on medium-low. Turn the sauce heat down to low and stir in the heavy cream. Stir gently until the sauce transforms into a silky, velvety mahogany-rose color and the meat is heated through.
Drop your cooked pappardelle or orecchiette directly into the pan with the sauce, tossing gently for a minute so the sauce clings to it.
Plate the pasta and finish each bowl with a generous dust of grated Parmesan cheese, a final crack of fresh black pepper, a pinch of flaky salt for texture, and a light drizzle of high-quality extra virgin olive oil.
