Bring a large pot of salted water to a boil and cook spaghetti according to package directions until al dente. Reserve 1/2 cup pasta cooking water, then drain and toss the pasta with a little olive oil to prevent sticking.
Heat 1 tablespoon olive oil in a large skillet over medium-high heat. Add the ground beef, chopped onion, chopped carrot, and chopped celery and cook, breaking up the meat, until the beef is browned and the vegetables are softened.
Add the minced garlic and sauté for about 30 seconds until fragrant, then drain any excess grease from the pan if necessary.
Stir in the crushed tomatoes, marinara sauce, balsamic vinegar, dried basil, chicken bouillon, sugar (to taste), salt, dried oregano, dried parsley, dried thyme, black pepper, and red pepper flakes (if using). Bring to a boil, then reduce heat and simmer uncovered.
Simmer the sauce gently for 10 minutes, stirring occasionally. If using, stir in the heavy cream and simmer an additional 5 minutes until the sauce reaches the desired consistency.
If the sauce is too thick, add reserved pasta water a little at a time until you reach the desired thickness.
Toss the cooked spaghetti with the Bolognese sauce or plate the pasta and spoon the sauce over it. Garnish with chopped fresh parsley and plenty of grated Parmesan before serving.