This article should help. I'd definitely go with something like protein pulsing with Mag-10 instead of just BCAA because of the more complete protein source and better absorption.
Also be sure not to overly-restrict calories or healthy fats (or high-quality protein from all sources, obviously). Your body is recovering, so give it ample nutrients. If you're concerned about getting pudgy while you're not training, dial back the carbs some (or most) days of the week.
Can you walk? Like, just plain old super-boring walking? Check with your doc first, but that might be good for morale, general energy, and recovery.