Begin by preheating your oven to 375°F (190°C). Allow the oven several minutes to fully heat so the buffalo chicken pockets bake evenly and develop a golden, lightly crisp exterior.
In a large mixing bowl, add the shredded cooked chicken, buffalo sauce, Greek yogurt, garlic powder, and shredded cheese. Use a spoon or spatula to mix everything thoroughly until the chicken is evenly coated and the ingredients form a creamy, well-combined filling.
Place the dough on a lightly floured work surface to prevent sticking. Use your hands or a rolling pin to gently roll the dough out until it becomes an even thickness. Then cut the dough into equal portions using a knife or pizza cutter so each pocket will be similar in size.
Take one portion of the dough and place it flat on the work surface. Spoon a small amount of the buffalo chicken mixture into the center of the dough, making sure not to overfill so the pocket can be sealed properly.
Carefully fold the dough over the filling, bringing one side over the other to create a pocket shape. Press the edges together firmly with your fingers or the back of a fork to seal the pocket completely so the filling stays inside during baking.
Line a baking sheet with parchment paper or lightly grease it with oil. Arrange the prepared pockets on the baking sheet, leaving a little space between each one so they bake evenly.
Using a pastry brush or spoon, lightly brush olive oil over the tops of the pockets. This helps the dough become golden brown and slightly crisp as it bakes.
Place the baking sheet in the preheated oven and bake the pockets for about 15–18 minutes. During baking, the dough will puff slightly and turn a beautiful golden color while the filling becomes warm and melty inside.
Once baked, carefully remove the pockets from the oven and allow them to cool for a few minutes before serving. This resting time helps the filling settle and makes the pockets easier to handle and enjoy.