Add onion, carrot, and celery to a food processor and pulse until they are finely minced.
Heat some oil in a large pot over medium-high heat. Add in the minced vegetables and cook until they are soft and starting to caramelize, around 5 minutes.
Add minced garlic to the pot and cook until it's fragrant, around 1 minute.
Add in the ground beef and cook until it's no longer pink, breaking it up as you go.
Pour in vermouth, bring to a simmer and cook until mostly reduced.
Stir in crushed tomatoes, tomato paste, beef stock, bay leaf, oregano, red pepper flakes, and balsamic vinegar. Mix everything together well and reduce the heat to a simmer. Let everything cook together for 45 minutes.
Stir in heavy cream to the pot. Bring the mixture to a simmer, stirring occasionally. Let it cook for about 45 more minutes, or until the sauce has thickened up nicely.
Season the sauce with salt and pepper to taste.
Cook rigatoni pasta according to package instructions. Drain and add it to the pot with the bolognese sauce. Toss everything together until the pasta is coated in the sauce.
Serve the pasta with some freshly grated Parmesan cheese on top.