1. Gather all your ingredients by finely dicing the onions and carrots, mincing the garlic, and grating the parmesan cheese, ensuring everything is prepped and ready for seamless cooking.
2. Heat butter or olive oil in a large skillet or Dutch oven over medium-high heat, then sauté the diced onions and carrots until softened and fragrant for 5-7 minutes.
3. Add the ground beef and optional Italian sausage to the skillet, breaking it into smaller chunks with a wooden spoon, and cook until fully browned, about 7-8 minutes. Drain any excess fat if necessary.
4. Stir in the minced garlic and cook for 1 minute before adding San Marzano tomatoes or crushed tomatoes and optional tomato paste. Combine well for a rich and flavorful sauce base.
5. Reduce the heat to low and let the mixture simmer, then stir in heavy cream or whole milk. Season with salt, pepper, and crushed red pepper flakes if desired, allowing the sauce to simmer for 20-30 minutes to develop its flavors.
6. Stir freshly grated parmesan cheese and chopped fresh basil or parsley into the sauce, keeping it warm while preparing the spaghetti.
7. Bring a pot of salted water to a boil and cook the spaghetti until al dente, following the package instructions. Reserve about 1 cup of pasta water and drain the rest.
8. In a large saucepan, melt butter over medium heat for the garlic butter sauce. Sauté minced garlic and optional diced onion until fragrant for about 2 minutes.
9. Add heavy cream and freshly grated parmesan cheese to the saucepan, stirring until the sauce thickens. Gradually add reserved pasta water to adjust consistency if needed.
10. Toss the cooked spaghetti into the creamy garlic butter sauce, gently coating each strand evenly. Season with salt and pepper to taste.
11. Plate the dish by adding a serving of creamy garlic butter spaghetti and topping it with a generous ladle of Bolognese sauce. Garnish with additional grated parmesan cheese and fresh basil leaves.
12. Serve and enjoy the rich, flavorful beef Bolognese paired with the creamy garlic butter spaghetti.