Recovery
Not all Harm is created equal. The difference isn't just in the numbers, but in how you get over it.
We've already said Hindrances require story solutions, not just dice. Dispel the blindness, cut the ropes, or find whatever narrative fix makes sense. Complications can be recovered whenever the GM says so. They might offer a recovery after a fight, when you get medical attention, after real rest, or when you do something that specifically addresses the problem. Any success at all wipes out explicit Complications entirely, or at least their modifiers.
Injury is typically recovered once per day, and usually only with proper food and rest. Roll against your current Injury total. Success reduces your Injury by the amount of effect you generate. Severe injuries take longer to heal because they fight back harder. The GM is completely within their rights to refuse most bonuses on this roll; Warriors train to do damage and avoid damage, not to sit quietly while it mends, so don't expect that Role to help.
Making It Dark
If you want a grittier, more dangerous and historically accurate world, you can treat them as opposition rolls and let the wounds bleed, or fester and worsen. This makes all Injury more dangerous and all healing more precious, but it makes the game more "realistic".
Second Wind
Players may say they want the character to back out of the fight for a minute to catch their breath. Even if it makes sense, it still isn't a Recovery. They might manage to catch a second wind, but that's just a roll for a Persistent Boost to negate the effect of some of their hurts, and it will go away at the end of the scene. The actual Recovery roll will still have to overcome all their damage. No Recovery Mid-Fight without Magick!