Heat oven to 400°F (200°C).
Place broccoli florets in a food processor and pulse until finely chopped; if you don’t have a food processor, finely chop the broccoli by hand.
Unroll the crescent dough onto a work surface and press perforations and seams to seal into one large rectangle.
In a small microwave-safe bowl, microwave the cream cheese on High for 30 seconds, then stir in the garlic powder until smooth.
Spread the cream cheese mixture over the dough, leaving a 1/4-inch border along one long side.
Evenly sprinkle the chopped broccoli over the cream cheese, then evenly distribute the shredded chicken on top.
Place a sheet of waxed paper over the filling and gently press to compress the filling into the dough.
Starting from the long side opposite the 1/4-inch clean border, tightly roll the dough into a log and pinch the seam to seal.
Using a sharp knife, cut the log into 8 equal slices and place each pinwheel cut side down in an ungreased 8- or 9-inch round pan.
In a small bowl, toss the coarsely chopped French fried onions with the melted butter until lightly coated; sprinkle the mixture over the tops of the pinwheels.
Bake for 18 to 22 minutes, or until the pinwheels are light golden brown.
Remove from oven and serve warm.