In a large skillet, heat olive oil over medium heat. Add the chopped onion and cook until translucent, about 3-4 minutes. Add the diced carrots and peas, cooking for an additional 5 minutes until tender.

Sprinkle the flour over the sautéed vegetables and stir well to combine. Gradually pour in the chicken broth, stirring constantly until the mixture thickens. Add the shredded chicken, garlic powder, onion powder, thyme, parsley, salt, and pepper. Mix until well combined and heated through. Remove from heat and let cool.

In a large bowl, combine the flour and salt. Add the chilled, cubed butter and mix with a pastry cutter or your fingers until the mixture resembles coarse crumbs. Gradually add cold water, one tablespoon at a time, mixing until the dough comes together. Divide the dough into two equal parts, shape into discs, wrap in plastic wrap, and refrigerate for at least 30 minutes.

Preheat your oven to 400°F (200°C).

On a lightly floured surface, roll out one disc of dough to about 1/8 inch thick. Cut into circles or squares, depending on your preference.

Place a spoonful of the chicken filling in the center of each pastry cut-out. Fold the dough over to create a pocket and seal the edges by pressing with a fork or your fingers.

Place the filled pastries on a baking sheet lined with parchment paper. Brush the tops with the beaten egg for a golden finish.

Bake in the preheated oven for 20-25 minutes, or until the pastries are golden brown and flaky. Remove from the oven and let cool slightly before serving.