Preheat the oven to 325°F (163°C).
Pat the short ribs dry and season them generously with salt and pepper. In a 5-quart (4.7-l) Dutch oven over medium-high heat, warm 1 tablespoon oil. Working in batches, add the short ribs and sear until browned on all sides, 4 to 5 minutes per side. Transfer to a plate.
Reduce the heat to medium and let the Dutch oven cool ever so slightly. Leave all that glorious mess of oil and drippings from searing the ribs in the Dutch oven. Add the onion and cook, stirring occasionally, until softened, about 8 minutes. Add the garlic and cook, stirring occasionally, until fragrant, about 1 minute. Add the bourbon and maple syrup and cook until reduced by half, 3 to 4 minutes. Stir in the broth, rosemary, tomato paste, and Worcestershire sauce. Nestle the short ribs in the sauce. The ribs should be almost completely covered with liquid; if necessary, add a little more broth or water (about 1/2 cup) to cover the ribs.
Increase the heat to medium-high and bring to a boil. Cover, transfer to the oven, and cook, stirring every 45 minutes, until the ribs are very tender, 2 to 3 hours. Transfer the ribs to a serving platter and cover loosely with aluminum foil and let them rest for at least 10 minutes.