Preheat an oven to 350 F.
Sear the beef. Pat the short ribs dry with a paper towel and generously season all over with salt and pepper. Add the oil to a dutch oven on medium-high heat. Once the oil is hot, sear the beef on all sides until browned. You may need to do this in batches. Remove the beef from the pan and transfer to a plate.
Saute the veggies. Decrease the heat to medium and add the butter. Add the diced onions, celery, and carrots to the pot and saute for 4-5 minutes, while stirring occasionally. You really want the veggies to brown a bit. Add the garlic and cook for another minute.
Mix the braising liquid. In a large measuring cup, whisk together the cranberry juice, dijon, beef stock, and beef bouillon paste.
Add the beef back to the pot. Nestle the short ribs and any accumulated juices into the veggies and pour in the braising liquid. It should reach about 3/4 of the way up the short ribs. Tie the fresh herbs into a bundle with kitchen twine and nestle them in the middle of the meat. Scatter the cranberries around the beef, cover and transfer to the oven.
Braise. Braise for 3 - 3 1/2 hours, until the beef is very tender. Remove from the oven and let it rest covered for 30 minutes. Discard the herbs and transfer the cranberry braised short ribs to a serving platter. At this point, you can thicken the braising liquid into a gravy, if desired. Season the braising liquid with salt and pepper before serving over mashed potatoes.