Finally made my short rib recipe over the weekend and what a great meal it makes!
You basically tackle it just like a stew - brown the meat, sweat off some onions and carrots. stir in a couple of tablespoons of tomato paste, a little flour then pour in a good half bottle of leftover (but still drinkable) wine. Bring to the boil, pour over the ribs (tucking in a couple of sprigs of thyme along the way and adding extra water to cover if you need) then cook over a very low heat or in a very low oven for 3 1/2 to 4 hours - it needs that long to render down the fat and make the meat fork tender.
Then, very important, cool the dish down and refrigerate it which makes it much easier to remove the layer of fat which will have accumulated on the surface. Underneath is the most wonderful jellied winey stock. Add another slosh of wine (about 75ml) before reheating and there you are.
The great bonus is that there is - or should be - a lot of liquid - enough to pour off some, strain it and freeze it to make an instant sauce for a couple of steaks or, more frugally, add instant oomph to a spaghetti bolognese or a cottage pie. In fact if you have any meat left over I'd advocate making the splendid French version hachis parmentier which contains a good handful of parsley which goes particularly well with the rich winey sauce.
If you think of this dish as a beefy equivalent to osso buco you'll get an idea of just how much the bones and fat contribute to its richness and depth of flavour. We had it with veg (mash and kale) but I think I would serve it with polenta on another occasion.