Prep the chopped ingredients (you can do this the night before) – carrots, celery, onion, and garlic.
In a large pot, heat 2 tbsp olive oil over medium-high heat. Add chopped carrots, celery, onion, thyme, and garlic. Cook vegetables until they’re soft.
Add beef chuck to the pot and break up the beef with a spoon. Cook meat and vegetables until the meat is browned.
Season with salt and pepper and add in red pepper flakes (if desired).
Add tomato paste and sauté for a couple of minutes.
Deglaze the pan with the diced tomatoes and allow to simmer for 30 minutes.
In another large pot, bring water to a boil and cook bucatini pasta until slightly al dente. Transfer cooked bucatini pasta to the Bolognese sauce. Add pasta water as necessary.
Add a couple pats of unsalted butter to the pasta and toss.
Plate bucatini bolognese and top with parmesan cheese, parsley, and more red pepper flakes (if desired).