Preheat the oven to 375°F (190°C).

In a mixing bowl, combine the cooked shredded chicken, softened cream cheese, chopped green onions, salt, and pepper. Blend until creamy.

Unroll the refrigerated crescent rolls, separate into triangles, and spoon the chicken mixture onto each triangle. Roll them up starting from the wide end.

Melt the butter in a small bowl, dip each rolled pillow into the melted butter, then roll in Italian-seasoned breadcrumbs.

Arrange the coated Chicken Pillows on a baking sheet lined with parchment paper and bake for about 12-15 minutes until golden.

In a saucepan over medium heat, melt the butter, then whisk in the flour for about 1 minute. Gradually add chicken broth and milk, whisking until smooth.

Stir in the grated Parmesan cheese with salt and pepper to taste, and simmer until thickened.

Remove the pillows from the oven and let cool slightly. Drizzle the creamy Parmesan sauce over the top before serving.