Preheat oven to 250°.Heat a dutch oven over a burner set to medium. Once hot, add just enough butter to cover the bottom, about a teaspoon. This is just to get things started, since the short ribs will release plenty of fat as the cook. Add the ribs and brown them for about ten minutes, turning regularly. Don't worry about searing every side.
Add wine, then cover. Bake for three hours. Then move the lid so that it is still on the dutch oven, but has a roughly 1" gap, and bake for another hour.
Check to make sure the meat is quite tender, then use tongs to remove it to a platter. Pour the broth from the dutch oven into a heat proof measuring cup or dish, and place it in the fridge.
Dice carrots and onion, then saute them in the dutch oven. There should be enough residual fat in it, but feel free to add some more butter if you're worried. Saute over medium low heat until the onion is translucent and the carrot has started to soften, about twenty minutes. Turn off heat.
Separate the short rib meat from the bones and fat. Place it in the dutch oven with the carrots and onions.
Check to see if the fat has solidified on the container of broth you put in the fridge. If it hasn't, place in the freezer for twenty minutes or so, then remove the fat from the top of the broth. Discard the fat.
Sprinkle salt and gelatin over the meat and veggies, then add the broth. Bring to a simmer, then cover and cook on low for 30 minutes, or until carrots are tender.
Serve with crispy potato wedges and a greens salad.