Bring a large pot of salted water to a boil and cook spaghetti until al dente according to package instructions. 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, finely chopped onion, carrot, and celery. Cook, breaking up the meat, until the beef is browned and the vegetables are softened, about 6–8 minutes.
Add the minced garlic and sauté for about 30 seconds until fragrant. Drain 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 chili flakes (if using). Bring the sauce to a boil, then reduce heat to a simmer.
Simmer the sauce gently, uncovered, for 10 minutes, stirring occasionally. If you prefer a thinner sauce, add reserved pasta water a little at a time.
If using, stir in the heavy cream and simmer 5 more minutes until the sauce reaches the desired consistency.
Toss the drained spaghetti with the Bolognese sauce or spoon the sauce over the pasta. Garnish with chopped fresh parsley and plenty of grated Parmesan before serving.