Your note just came and am utilizing a good hangover to answer it. I was not annoyed at anything you said (You surely know by now, I’ve written it often enough, how much I admire your work). I was only annoyed at your refusal to accept the sincere compliment G. Stein was making to you and instead try and twist it into a slighting remark. She was praising her head off about you to me when you came up she started to repeat it and then at the end of the praise to spare you blushes and not be rude to me she said that our flames (sic) were maybe not the same—then you brood on that—
This is the first paragraph of Ernest Hemingway's letter to F. Scott Fitzgerald. I looked up the dictionary for the phrase "head off" but still don't understand what does "praising her head off" mean in this context.