I remember back in between 2006-2010 when i did alot of pull up every day , the strength for making a pull up with 1 hand came from itself !
Do pull ups every day as much as u can with no more than 45sec. - 1min. rest between sets and do every set with maxium reps with all types of grips
10 sets - max reps with Standart pull up , 45sec. - 1min. rest between each set , every day
6 sets - max reps with Neutral grip , 45sec. - 1min. rest between each set , every day
6 sets max reps with Chin ups , 45sec. - 1min. rest between each set , every day
3-4 sets of just hanging for atleast 45sec. - 1min. per set , every day