1. Prepare the filling ingredients: In a large mixing bowl, combine the shredded or diced cooked chicken, finely chopped fresh broccoli florets, shredded cheddar cheese, softened cream cheese, milk, and garlic powder. Season with salt and black pepper to taste. Mix everything thoroughly until all the ingredients are well combined and the cream cheese is evenly distributed, creating a creamy, cohesive filling.

2. Preheat and prepare the baking sheet: Preheat your oven to 375 F (190 C). Line a large baking sheet with parchment paper for easy cleanup, or lightly grease it with cooking spray. This will prevent the crescent rolls from sticking and ensure they brown beautifully.

3. Unroll the crescent dough: Carefully open the can of refrigerated crescent rolls. Unroll the dough and separate it into 8 triangles along the perforations. Lay them flat on your prepared baking sheet.

4. Fill each crescent triangle: Place a generous spoonful (about 2-3 tablespoons) of the chicken and broccoli mixture onto the wider end of each crescent roll triangle. Make sure not to overfill, as this can make rolling difficult and cause the filling to spill out during baking.

5. Roll up the crescent rolls: Starting from the wider end, carefully roll each crescent triangle towards the pointed end, enclosing the filling. Gently tuck in the sides as you roll to seal the filling inside. Arrange the rolled crescent pastries on the baking sheet, leaving a little space between each one.

6. Bake until golden: Place the baking sheet in the preheated oven. Bake for 18-20 minutes, or until the crescent rolls are puffed up, beautifully golden brown, and the cheese inside is melted and bubbly. The exact baking time may vary slightly depending on your oven.

7. Serve immediately: Once baked, remove the crescent rolls from the oven. Let them cool for a few minutes on the baking sheet before transferring them to a serving platter. They are best enjoyed warm, when the cheese is still gooey and the crescent dough is at its flakiest.