Preheat oven to 350°F (175°C). Grease a large baking sheet or line it with parchment paper.
In a large bowl, combine 4 cups shredded chicken, 8 ounces softened cream cheese, ½ cup milk, ¼ cup grated Parmesan, 2 cloves garlic (pressed or minced), 1 teaspoon dried oregano, ½ teaspoon dried basil, ¼ teaspoon dried thyme, and ¼ cup chopped green onion. Stir until the mixture is evenly combined and spreadable.
Unroll one package of crescent rolls on a clean surface. Press the diagonal seams together to seal the perforations, then separate the dough into 4 equal rectangles. Repeat with the second package so you have 8 rectangles total.
Divide the chicken mixture into 8 equal portions. Place one portion in the center of each rectangle.
Pull the dough edges up and over the filling, pinching and sealing to form a closed round “pillow.” Place each pillow seam-side down on the prepared baking sheet, spacing them a couple inches apart.
Brush the top of each pillow with 1 tablespoon melted butter, then evenly sprinkle ¼ cup Italian breadcrumbs over the tops.
Bake for 18–23 minutes, or until the dough is cooked through and the tops are golden brown.
Remove from the oven and let the pillows rest on the baking sheet for about 5 minutes before serving.