Mix the flour with a generous amount of salt and pepper on a sheet of waxed paper. Pat the roast dry; dredge it in the flour mixture on all sides.
Heat butter and olive oil in a large Dutch oven (at least 6 quarts or larger) over medium-high heat until it is hot but not smoking. Brown the meat to give it nice color (about 5 minutes per side). Transfer the meat to a plate.
Reduce the heat to medium and add 1 cup of the beef broth, scraping with a wooden spoon to deglaze the pan (loosening all the browned bits from the bottom). Add the onions, carrots, celery, and garlic to the pot. Cook, stirring, until the onions are translucent (about 10 minutes).
Place the roast on top of the vegetables. Add the remaining two cups of beef broth, red wine, thyme, rosemary, and bay leaves. The liquid in the pot should come about halfway up the side of the roast. If necessary, add water or extra broth to reach this level. Bring the mixture to a simmer. Season with salt and pepper, cover with a lid, and reduce the heat to medium-low.
Simmer the mixture gently on the stovetop for about 3 hours, or until the beef is fall-apart tender when pulled with a fork. As the roast cooks, occasionally check the pot to make sure that the liquid stays at a similar level (adding extra water or broth as necessary). Adjust the temperature to keep the liquid at a gentle simmer, but not a boil (you might need to simmer the pot over low heat instead of medium-low heat).