BBQ here in Brazil has remained a mystery to me. Frankly, I cut my teeth as a cook in college when I cooked for a 20 person vegetarian co-op (where I lived) and worked for a vegetarian hippy day care center (peanut butter pizza with peas). I later took a job as cook in a fraternity - but I always screwed up the hamburgers.
So don´t listen to me about Brazilian BBQ. But check out this link to a fantabulous explanation on how to cook picanha. It solves the mystery!