Prepare the Bolognese Sauce:
In a large skillet or Dutch oven, heat a bit of oil over medium heat.
Add the chopped onion, carrot, and celery. Sauté until the vegetables are soft and the onion is translucent.
Add the minced garlic and cook for another minute until fragrant.
Brown the Meat:
Add the ground beef to the skillet. Cook until browned, breaking it up with a wooden spoon as it cooks.
If using red wine, add it to the skillet and let it simmer for a few minutes until the liquid reduces slightly.
Add Tomatoes and Seasoning:
Stir in the crushed tomatoes, beef broth, tomato paste, dried oregano, basil, thyme, salt, and pepper.
Bring the mixture to a boil, then reduce the heat to low and let it simmer uncovered for at least 45 minutes, stirring occasionally. The longer it simmers, the better the flavor.
Finish the Sauce:
Stir in the heavy cream and let the sauce simmer for another 10 minutes.
Cook the Spaghetti:
While the sauce is simmering, bring a large pot of salted water to a boil.
Add the spaghetti and cook according to the package instructions until al dente. Drain the spaghetti in a colander.
Combine and Serve:
Toss the cooked spaghetti with the Bolognese sauce until well combined.
Serve the Bolognese Spaghetti hot, topped with freshly grated Parmesan cheese and garnished with fresh basil or parsley.