Do they have Magical healers in the Dresdenverse? Harry makes it sound like Healing Magic is next to impossible.
It's pretty damn rare. The only instance we have of it on the page is healing done by one of the Queens of the Summer Court, and she's operating with a power source that's way off the scale.
What about Lea? Didn't she do some healing too?
Okay, so so far we're talking about a highly-placed noblewoman of the Winter Court, and one of the Summer Ladies herself.
Neither of those are player character concepts. They're NPCs.
Oh, and whoever has the Shroud of Turin at the moment.
Or a relic of comparable power. Scriptural references follow:
2nd Kings 13:
"20 Elisha died and was buried.
Now Moabite raiders used to enter the country every spring.
21 Once while some Israelites were burying a man, suddenly they saw a band of raiders; so they threw the man's body into Elisha's tomb. When the body touched Elisha's bones, the man came to life and stood up on his feet."
Acts 19:
"11 God did extraordinary miracles through Paul, 12 so that even handkerchiefs and aprons that had touched him were taken to the sick, and their illnesses were cured and the evil spirits left them."
On a more Dresden-related note, blood rites page 251, Lord Raith heals himself (yes, he's a vampire lord, but he's been weakened significantly [trying to avoid spoilers]):
Then Raith's flesh began to glow. His shirt was in shreds, and he tore it from him with a negligent gesture. His skin became suffused with a pale light once more, and I saw his body rippling weirdly around an ungainly hole left of his navel. He was healing. I stared at him tiredly for a minute, then bent over and picked up my sword. He laughed at me. "Dresden. ..."
Thomas pulls the same trick in a later book, iirc.