Preheat your oven to 375°F.
In a medium bowl, combine the chopped broccoli, shredded cheddar cheese, cream cheese, garlic powder, onion powder, salt, and black pepper. Mix until well combined.
Unroll the crescent roll dough on a lightly floured surface and pinch the seams together to create a solid rectangle.
Spread the broccoli and cheese mixture evenly over the dough, leaving a small border around the edges.
Starting from one long side, carefully roll the dough up into a tight log. Pinch the seams to seal.
Slice the log into 1-inch pinwheels and place them on a baking sheet lined with parchment paper.
Brush the tops of the pinwheels with the beaten egg for a golden finish.
Bake in the preheated oven for 15-20 minutes, or until the pinwheels are golden brown.
Let cool for a few minutes before serving.