1. Line 2 baking sheets with parchment. On a lightly floured surface, roll pastry pieces into 4 6-inch squares. Place on 1 baking sheet, cover and chill.
2. Melt butter in a skillet over medium heat. Sauté onion until softened, about 3 minutes. Add peas and carrots; sauté 3 minutes. Sprinkle thyme and flour over vegetables; sauté 1 minute. Raise heat to medium-high. Stir broth and mustard into pan. Add chicken; cook until sauce is thick, 7 to 10 minutes. Transfer to a bowl; let cool. Season with salt. Preheat oven to 375ºF.
3. Place 1 pastry square on reserved baking sheet. Brush edges with egg. Spoon 1/4 of chicken mixture into center; fold to form a triangle. Seal edges. Repeat with remaining pastry and filling. Brush with remaining egg. Cut 3 slits in top of each. Chill for 15 minutes.
4. Bake turnovers until golden, about 30 minutes. Let cool 5 minutes and serve.