Preheat your oven to 375°F (190°C) and line your baking sheet with parchment paper.
In a large bowl, mix together the shredded chicken with softened cream cheese, garlic powder, onion powder, dried parsley, salt, black pepper, and melted butter until well combined and creamy.
Unroll the crescent roll dough and separate it into eight individual triangles. Lightly press each triangle down to flatten them slightly.
Spoon a generous portion of the chicken mixture onto the wide part of each crescent triangle. Fold over the edges and pinch them together firmly to seal.
Brush each filled pillow with beaten egg and sprinkle panko breadcrumbs over each pillow if desired.
Place the chicken pillows on the lined baking sheet and bake for about 20–25 minutes until golden brown.
In a saucepan over medium heat, melt butter and whisk in flour until slightly golden. Gradually add milk and heavy cream while whisking until smooth. Stir in grated Parmesan cheese, garlic powder, salt, and black pepper, and let it simmer until thickened.
Drizzle the baked chicken pillows with the creamy sauce before serving.