No! The fat is where the flavour comes from! Cook the short ribs according to the recipe and let it cool then skim the fat off the top. I've found that to be the easiest way to remove the large amount of fat that comes out.
I had a similar experience to you, westie, the place was empty for lunch yesterday but it was a gorgeous day and my friend and I sat in the garden and had a lovely meal: arugula salad, the housemade papardelle with mushrooms (yummy!) and we couldn't leave without trying the lemon tart (yummy x 2!). The whole meal was perfectly done and the service was just right, attentive but not too on top of us. Although I'd heard about this place a while ago, I'd never tried it (not being a huge fan of Italian food) but this exceeded my expectations! I almost hope it doesn't become too popular.......!
Also, there is parking in the lot across the street (the area around the restaurant is all permit parking).