Preheat oven to 375°F (190°C) and line a baking sheet with parchment paper.
In a skillet, heat olive oil and sauté onion and garlic until soft. Add chicken (or beef) and vegetables. Season with herbs, salt, and pepper. Remove from heat, stir in cheese, and let cool slightly.
Roll out pastry and cut into 8 circles or rectangles. Place filling in the center of each piece.
Fold over and crimp edges with a fork to seal. Brush tops with egg wash.
Place on the prepared baking sheet and bake 20–25 minutes, until golden and puffed.
Serve warm with dipping sauces.