I believe generals recover Hit Points immediately after the battle is over. I've yet to find a way to look in-game at the general's personal Hit Points, since the Hit Points on his unit card refer to that of his Bodyguard and not the the general himself. Bonus Hit Points are listed under the general's Traits on the campaign map, so I tend to keep a running tally of those as the campaign progresses.
York: A Case Study
In my experience, taking York on the first turn of an English or Scottish campaign is the best way to rapidly build up the beginnings of a warmonger general. Recently I sent the Scottish faction heir with a unit of border horse to take the settlement, with excellent results.
York has two units of archers, two of peasants, and one of spear militia -- a large number of low-powered units, just the sort of stack you want. It's doubly useful since it doesn't have walls, allowing you to charge the gates on the first turn. Seeing this, I let by Border Horse hang back and provide occasional support while my General's Bodyguard did the cleaning. Over the course of the battle, I intentionally shaved by contingent of Bodyguards down to half a dozen men, drawing the militia out and killing undefended stragglers. Rather to my amazement, I pulled off a victory with only one Bodyguard left fighting alongside by General and no surviving border horse. The results for the proud Prince Canmore:
Maximum experience (three gold chevrons) starting from one bronze chevron.
Promising Commander (+1 Command)
Feels Appreciated (+1 Loyalty)
Fierce in Battle (+1 Dread, +1 morale for all troops on the battlefield, +1 command when attacking, -1 command when defending)
Wall Taker (+1 Command when assaulting walls)
Good With Cavalry (+1 Command when commanding cavalry)
Marks of War (+1 Authority, +2 Hit Points)
Brave (+1 morale for all troops on the battlefield)
Swordbearer (+1 personal security, +1 Hit Points)
Veteran Warrior (+1 personal security, +1 command when commanding infantry)
Not bad for fifteen minutes' work on the killing field, aye?
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