Elvis didn't invent "cool."
“Sprezzatura” is a term coined by Baldassare Castiglione in 1528 in The Book of the Courtier. It describes the cool, confident attitude often expressed in the portraiture of the time. The classic example is Raphael’s portrait of Castiglione himself.
Illustrator Shirley Hughes, in her memoir A Life Drawing suggests that discoveries of serious-looking Roman busts during the Renaissance led to a taste for the "devil may care" look in portraiture.
The word is related to the Italian “sprezzante,” meaning contemptuous or scornful, used here in the sense of disdaining effort. The goal is a certain nonchalance or carelessness, as if one’s mastery arrived almost by accident, and certainly not through any struggle.
At various times in history, artists have tried to capture this particular attitude, both in the disposition of their subjects and in their handling of paint. Sargent accomplished it in his portrait of his teacher Carolus Duran.