Short ribs are just as they sound—short, wide and almost square; the meat will shrink on the bone as it cooks, but will wind up meltingly tender.
Heat a drizzle of oil in a heavy skillet or oven-proof pot set over medium-high heat. Season the ribs with salt and pepper and brown on all sides; set aside. Add the carrot to the pan and cook for a few minutes, then add the garlic and cook for another minute. Pour in the balsamic vinegar and cook for a minute, scraping up the browned bits from the bottom of the pan.
Return the browned ribs to the pan with the vegetables. Add enough stock to come about halfway up the sides of the ribs. Cover and cook at 300˚F for 2 hours. Add the lentils to the pan, and a little more stock so that there’s enough to generously cover the lentils, cover and return to the oven for another 30 minutes, or until the lentils are tender and the meat is very tender.
Serve the ribs with the lentils, on mashed potatoes if you like.