Heat the olive oil in a 4 to 5-quart pot on medium-high heat. Add the onions and cook for 2 minutes. Add the garlic and cook for 30 seconds longer or until fragrant.

Add the carrots and mushrooms, and cook for 2 minutes. Add the tomato paste, stir to blend, and cook for a minute longer.

Add the canned tomatoes, parsley, and basil. Mash and stir the tomatoes with a potato masher until the sauce starts to thicken, about 5 minutes over medium-high heat.

Reduce the heat to low and simmer gently while preparing meatballs, stirring occasionally.

In a large bowl, use your hands to mix the beef, Italian sausage, basil, parsley, mushrooms, eggs, breadcrumbs, cheese, salt, and pepper. Do not over-mix or the meatballs will be tough.

Use a small melon baller, cookie scoop, or heaping teaspoon to form 1-inch round meatballs. Roll and compress into tight balls, but don't overwork the mixture.

In a separate wide, shallow pan, heat the olive oil on medium-high heat. Brown the meatballs on all sides, about 2 to 3 minutes.

Depending on pan size you may need to brown 2 batches of the meatballs. Cook them in a single layer; do not crowd the pan by stacking them.

Do not overcook the meatballs; they will continue to cook in the sauce. You just want to brown them on all sides. Towards the end of browning the meatballs, add a little bit of red wine to deglaze the pan.

Add the red wine to the sauce and stir in the cheese. Add salt to taste. Add the browned meatballs and gently stir. Simmer the sauce and meatballs for 30 to 45 minutes, stirring occasionally.

While the sauce is simmering, bring a large pot with 4 quarts of salted water to a boil (1 tablespoon of salt for every 2 quarts of water). When the water returns to a boil add the pasta to the pot.

Leave the pot uncovered while you cook the pasta on high heat with a vigorous boil. Put a timer on for 8 to 10 minutes, or according to package directions for al dente pasta (cooked but still a little firm). Drain.

To serve, place a thin layer of sauce on each plate, add the pasta, add sauce and meatballs, and then sprinkle with grated Parmesan-Romano cheese.