Trim the asparagus of their tough bottom thirds and, if they're thick, peel off their skins. (Slimmer asparagus don't need peeling.)

Parboil the asparagus in well salted water until just slightly underdone. Drain and set aside until needed. 

In a skillet large enough to hold the asparagus in a single layer, sauté the prosciutto and mint in the fat of your choice over moderate heat, just until the prosciutto has turned color and the mint leaves have wilted.

Transfer the parboiled asparagus to the skillet and let them simmer in the seasoned fat for just a few minutes, long enough for them to absorb the flavors and become fully tender. Toss from time to time.Add the remaining mint leaves and toss the asparagus once or twice more.

Serve while still warm.