Season the short ribs all over with salt and pepper then dust with flour. Heat a 7-quart Dutch oven over medium-high heat, add the olive oil and heat through.
Working in batches, sear the ribs on all sides, about 5 minutes total. Remove to a plate and repeat with the remaining ribs.
Return the pot to medium heat and add the onion, celery and carrot, sautéing until tender, about 6 minutes. Stir in the tomato paste and thyme then add the garlic, bourbon, maple syrup and beef stock. Return the short ribs to the pot and bring to a boil over medium heat.
Cover the Dutch oven and move it to the oven and cook, turning the ribs occasionally, until the meat is fork tender, about 3 to 3½ hours. Squeeze the garlic cloves into the braising liquid and stir in vinegar.
(Optional): Remove the short ribs and thyme sprigs. Skim the fat from the braising liquid then add to a blender and blend until smooth so it's thicker to easily spoon over the top of the short ribs.
Arrange one short rib on each plate over mashed potatoes and roasted vegetables. Ladle the additional sauce over the top of the short ribs and serve.
Notes
Taking the extra step to blend the braising liquid adds an incredible smooth sauce to the short ribs.
Refrigerate short ribs in an airtight container for up to 4 days, or freeze for up to 2–3 months. Thaw before reheating by gently simmering in the sauce to keep them moist.