Love short ribs. All these recipes kinda touch around the basics.
I like to use carrots, celery, onion, lots of garlic and herbs in the cooking liquid of red wine and stock, then reduce and strain the sauce a little before serving. May even pulse it in the blender once or twice if I get the urge.
I use the Emeril Lagasse method of smashing some of the vegetables against the side of the roast pan or dutch oven with a spoon to thicken the sauce a bit.
Pure goodness in the end.