Preheat oven to 450°F.

Lightly flour a surface.

Divide pizza dough into four equal pieces.

Roll or stretch each piece into a 6-inch round.

If dough shrinks, let it rest for 5 minutes, then roll again.

Divide mozzarella cheese among the dough rounds.

Top equally with pesto, broccoli, and chicken.

Gently pull half of dough over filling to make a half-moon shape.

Fold bottom edge over top edge and pinch firmly to seal.

Brush calzone tops lightly with olive oil.

Transfer to a large baking sheet.

Bake calzones on middle rack until golden brown, 20 to 25 minutes (15 to 20 minutes in a convection oven).

Let cool about 5 minutes, then transfer to plates.