Ok, getting back to the OP...
I think that recipe is a bit messed up. Mind posting the whole thing?
When I'm going to braise something I'll brown the meat in a pan and add them on top of the vegetables I'm using to the pot. Deglaze the pan with some pinot and scrape up the good bits. Cover and simmer till tender (hour and a half-ish?).
Once that is done and I want a thicker sauce or gravy, then I will make a roux/beurre manie/slurry and thicken it up