Preheat oven to 400 degrees F (200 degrees C). Line 2 baking sheets with aluminum foil; grease with cooking spray.
Melt butter in a large skillet over medium heat. Cook and stir spring onions and garlic until tender, about 5 minutes. Add chicken; cook and stir until no longer pink in the center, about 5 minutes. Season with salt and pepper. Remove from heat and let cool, about 10 minutes.
Arrange pastry discs on a flat work surface. Dab a little water around the rims. Place a large tablespoonful of the chicken mixture in the center; fold pastry over and press with a fork to seal.
Transfer empanadas to the prepared baking sheets. Brush beaten egg over the tops.
Bake in the preheated oven until golden, 10 to 15 minutes. Let cool for 5 minutes before serving.