Trading Pieces

The other day at a chess club I practiced with the students how to checkmate with a queen and a rook or with two rooks. After the lesson one of the kids in the class was ahead by a queen and a rook, but was unsure what to do. I suggested that he should make fair trades to try to get into a position where he could do the queen and rook checkmate. Later on I looked at the game and noticed that one player had more pawns than he used to have and was missing a bishop. The players explained that they had simply negotiated a fair trade just as I had suggested.

As a puzzle for more experienced players than those in the story, how can white make a fair trade or better here in order to extinguish black’s initiative?