Preheat oven to 400 degrees. Prepare baking sheet by lining with parchment paper. Set aside.
Cook broccoli in microwave according to package instructions. Measure out 1 cup of cooked broccoli and chop it into smaller pieces. Save remaining broccoli for another use.
Roll out puff pastry into a 10x10 inch square. Spread cheese cheese all over using an offset spatula to ensure the layer is even. Sprinkle evely with broccoli pieces and shredded cheese. Taking the edge closest to you, roll up pastry dough to create a log. Cut the log into 8 even pinwheels (16 if you intend to serve these as an appetizer and want smaller portions). Place the pinehweels on a prepared baking sheet and place in the freezer for 5 minutes before baking.
Remvoe from the freezer and bake in preheated oven for 25 minutes or until the pastry turns golden brown and the centers looked cooked. Remove from the oven and cool for 5 minutes before serving.