Bring a large pot of salted water to a boil and cook spaghetti until al dente according to package directions; reserve 1/2 cup pasta cooking water, then drain and toss 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, carrot, and celery and cook, breaking up the meat, until the beef is browned and the vegetables are softened.
Add the minced garlic and sauté about 30 seconds until fragrant, then drain excess fat from the pan if desired.
Stir in crushed tomatoes, marinara sauce, balsamic vinegar, dried basil, chicken bouillon, sugar, salt, oregano, dried parsley, dried thyme, black pepper, and red pepper flakes (if using).
Bring the sauce to a gentle boil, then reduce heat and simmer uncovered for 10 minutes, stirring occasionally.
If using, stir in the heavy cream and simmer 5 more minutes until the sauce reaches your desired consistency; add reserved pasta water a tablespoon at a time if you prefer a thinner sauce.
Serve the Bolognese sauce over the cooked spaghetti and garnish with fresh parsley and plenty of Parmesan cheese.
