Arrange rack to center of oven and preheat oven to 350F (165C).
Season beef on all sides with salt and pepper.
Heat oil in a large enameled Dutch oven over medium/high heat. Once oil is shimmering, add beef and sear on all sides until deep brown in color (once you place the beef in the pot, let it sit for about 2-3 minutes before touching/turning it so you get a nice sear). After searing, remove to a plate and set aside. There should be lots of browned bits on the bottom of the pot – leave those, they’re great for flavor.
Reduce heat to medium. Add butter to the pot and, once melted, add carrot, celery, and onion and cook, stirring occasionally, until softened (about 3-5 minutes).
Add garlic and cook, stirring frequently, until fragrant (about 30 seconds).
Add tomato paste and stir until well-incorporated with veggies.
Deglaze the pan by slowly pouring in red wine vinegar and scraping the bottom of the pan to loosen any brown bits. Cook until the vinegar is reduced by about 50% and the steam from the pot no longer has a pungent vinegar odor.
Add beef broth, water, crushed tomatoes, and crushed red pepper (if using). Bring to a simmer, stirring occasionally.
Return beef to the pot and add bay leaves and thyme (make sure they are submerged), cover with lid, and transfer to the oven.
Cook for 3 hours or until beef is extremely tender and may be easily shredded with a fork (but don’t shred it yet).
Remove beef from the pot. Use a potato masher to break up the vegetables in the pot (for a smoother sauce, use an immersion blender, but I like mine a bit heartier). Shred the beef and return to the pot. Taste-test and add additional salt/pepper as needed.
Serve as desired, I like to serve mine over pappardelle. If you’d like to toss the noodles with the bolognese sauce, reserve a bit of the pasta water (about ½ cup) and add it into the sauce with the noodles and simmer over low heat for several minutes until thickened and clinging to the noodles before serving. Top with freshly grated parmesan cheese.