Preheat your oven to 375°F (190°C) and lightly grease a baking sheet or line it with parchment paper.
 In a large mixing bowl, combine the shredded chicken, softened cream cheese, chopped chives, garlic powder, onion powder, salt, and pepper. Mix well until the ingredients are thoroughly combined.
 Unroll the crescent roll dough and separate it into triangles. Place about 2 tablespoons of the chicken mixture in the center of each triangle and fold the dough over the filling, pinching the edges to seal and form a pillow shape.
 Place the prepared chicken pillows on the baking sheet, leaving space between each. Brush the tops with cooking spray or melted butter for a golden finish.
 Bake in the preheated oven for 12-15 minutes or until the dough is golden brown and fully cooked.
 While the chicken pillows are baking, prepare the creamy Parmesan sauce. In a saucepan, melt the butter over medium heat. Stir in the flour and cook for 1-2 minutes until lightly golden.
 Gradually whisk in the chicken broth and heavy cream, ensuring there are no lumps, and bring the mixture to a simmer.
 Add the grated Parmesan cheese and nutmeg, stirring until the cheese is melted and the sauce is thickened. Taste and adjust seasoning with additional salt and pepper if desired.
 Remove the chicken pillows from the oven and let them cool slightly before serving.
 Serve the chicken pillows drizzled with the creamy Parmesan sauce, or on the side for dipping.