Season all sides of the short ribs with salt and pepper and set aside. Place flour in a gallon-size re-sealable bag then add the ribs and shake to lightly coat them in flour.
Next, heat olive oil in a large Dutch oven over medium-high heat until the oil is shimmering. Add as many short ribs as possible without overcrowding the pan. Brown the ribs on all sides then transfer to a plate and keep warm. Repeat with remaining short ribs.
Once the last of the short ribs has been transferred, immediately add butter and reduce the heat to medium. Add the onions and allow them to cook for approximately 3 minutes before adding the garlic. Allow the garlic to cook approximately 2 minutes then add the beef broth and red wine. Begin scraping the bottom of the skillet to remove anything that may be sticking.
Simmer the broth and wine for about 5 minutes before adding the remaining ingredients. Stir until combined then add the short ribs to the Dutch oven. Cover and put the Dutch oven in the oven and roast for about 2½ hours.
When the ribs are fall-apart tender, carefully remove them to a serving platter and strain the cooking liquid through a sieve. Allow approximately 2 minutes for the fat to rise to the surface then skim it off with a ladle. Pour the liquid over the short ribs and serve. Enjoy!