Preheat your oven to 400°F (200°C) and line a baking sheet with parchment paper.
In a mixing bowl, combine the chopped broccoli, grated cheddar cheese, salt, and black pepper.
Roll out the puff pastry sheet on a floured surface and cut it into squares.
Place a spoonful of the broccoli and cheese mixture onto each square of puff pastry.
Cut into small squares and place the filling in the center of each square.
Place the puffs on the prepared baking sheet and brush the tops with the beaten egg.
Bake in the preheated oven for 20-25 minutes, or until the pastry is golden brown.
Remove from the oven and let cool slightly before serving.