Special equipment: An immersion blender.
Heat a large skillet over high heat until smoking hot. Reduce the heat to medium-high and add the oil. Add the ground beef and Italian sausage, breaking up the pieces with a wooden spoon, and cook until brown, about 10 minutes. Add the onions and garlic and saute for 3 minutes. Transfer the browned-meat mixture to a strainer and discard the fat.
Add the heavy cream to the drippings in the skillet and cook, scraping up the brown bits with the wooden spoon, until reduced by one quarter, 2 to 3 minutes. Reserve. Transfer the meat to a large pot. Add the Pasta Sauce and heavy cream mixture, bring to a simmer and cook until the flavors have melded, about 30 minutes.
Combine the whole peeled tomatoes, extra-virgin olive oil, basil, carrot, oregano, onion and garlic in a large saucepan and pulse with an immersion blender. Bring the sauce to a simmer and stir in the diced tomatoes, tomato paste, salt and pepper. Simmer until the carrots are tender, 20 to 30 minutes.