Preheat the oven to 375 degrees F.
Line a baking sheet with parchment paper or a silpat liner. Set aside.
Melt the butter in a large sauté pan over medium heat. Cook the onions, and celery with salt, pepper, and thyme, until softened, about 10 minutes.
Add the garlic and cook for an additional minute, until fragrant, stirring frequently.
Add the flour and cook off the raw flour taste, about 1 minute more.
Add wine and deglaze the pan scraping up the browned bits in the bottom of the pan.
Stir in the chicken broth and Dijon mustard.
Add the diced chicken and frozen peas & carrots. Bring mixture to a simmer. Cook on a very low simmer until the sauce thickens up into a thick gravy, about 5 to 10 minutes.
Remove from the heat and set aside.
On a lightly floured surface, unfold the pastry dough and gently roll out , increasing the size about 20 percent.
Cut pastry dough into 4 squares.
Spoon the chicken mixture in the center of each square.
Fold the squares kin half diagonally to create triangles. Press the edges together to create turnovers. Press the edges together with a fork to create a decorative border and seal turnovers.
Whisk the egg with a splash of water and brush the turnovers with the egg wash.
Cut a small slit in the top of each turnover to allow steam to escape during baking.
Bake the turnovers until golden brown, about 25-30 minutes.
Remove turnovers from the oven and let cool at least 10 minutes before serving.
Serve with a crisp green salad to round out the meal.