My favorite beef rib is from the 7-bone whole beef rib (prime rib or bone-in rib eye), separated from the rib eye...but, I've never removed the membrane from slabs..easy to bite around it with long bones...it should be easier to remove from a larger slab than short ribs, though. I've read that a paper towel helps to grip the edge of the membrane once you lift it up a bit with a blade, then grab with the towel to slowly and gently peel it off.
Boneless rib eye on top, ribs below:
Cut from an 18lb whole beef rib...this slab was 5.5lb precooked weight:
A rather large and juicy appetizer before dinner:
The fixings for the main course...precooked weight was 12.6lb:
Med-rare:
Smoked Russet on the side, drizzled with it's own juices from the board (no Au Jus needed here):
I couldn't resist the temptation to post pics...just a teaser to nudge you into pulling the trigger on one, I guess...LOL!!! Seriously though, this is the best cut of beef at an affordable price when it's on sale. Last week, they went on sale for $3.99lb in a nearby grocery chain here (reg. $8,99-10.99lb)...crazy low sale-price, especially when chuck has been $3,89/lb regular, lately. I hope lots of other areas offer good sales on them like this. Even for our family, a 7-bone whole beef rib can make 3 meals: Ribs for lunch, 1/2 the rib eye for dinner, and steak-out the other half of the rib eye to marinade overnight for dinner the next evening. This particular beef dinner was $4.49lb, $81.31...not something for a once per week meal, but a darn fine treat to have a few times per year, and is a Christmas tradition here as well.
EDIT: btw, if it's the heavy connective tissue on the bone you're talking about, there's not much you can do about that except to cook them low & slow for a bit longer to get it to melt away a bit more.
Eric