Preheat the oven to 400F. Line a baking sheet with aluminum foil and coat it with non-stick spray.
Pat chicken breast pieces dry and sprinkle some salt and pepper on both sides. Place on the baking sheet.
Bake in the oven for 20-25 minutes until fully cooked. Let chicken breast pieces cool completely then shred them using two forks.
Turn the oven temperature to 350F.
Place 24 squares of puff pastry in two baking sheets lined with parchment paper. Cut a small square out of 12 of the squares so you have 12 frames.
Using a pastry brush, brush some egg on the edges of puff pastry squares, then place the 12 puff pastry frames on the squares. Poke the bottom puff pastry 3-4 times using a fork. Bake in the oven for 15 minutes or until golden brown and puffed. Let the "puff pastry cups" cool completely.
In a large bowl, mix shredded chicken, walnuts, chopped green onion, mayonnaise, Greek yogurt , salt and pepper.
Fill the cups with chicken mixture and serve either cold or at room temperature.