Preheat oven to 350 F (175 C).
Cut your short ribs into large pieces, I usually try to have one bone in each chunk which ends up with about 3-inch square pieces. Liberally season each short rib piece with salt and pepper. In a large oven-safe pot or dutch oven, brown your short ribs over medium-high heat until all sides are brown. This should take less than 10 minutes. If you have too many short rib pieces to comfortably brown, you may want to sear your short ribs a few at a time. When each one is brown on all sides remove to a plate to rest.
Saute your chopped onions in the same pot that you browned your short ribs. You will want to cook them for about 5 minutes.
Add your garlic and tomato paste and heat that up, stirring often for 2 minutes.
Add beer, Worchestershire sauce, and all of your beef broth.
Put your resting short ribs back into the pan with all the sauce. Roll them around to coat.
Place the pot in the oven for 3 to 3.5 hours to braise.
Remove the pot from the oven and allow the short ribs to cool for at least 20 minutes before serving.
Notes:
For the beer choice, I would shoot for a non-bitter beer. Maybe an amber (if you can find one) or something malty like a brown ale or dark lager. I used a pilsner that was fairly hoppy in my most recent batch and you could taste a slight bitterness from the hop flavor being reduced after 3 hours of braising.