Preheat your oven to 375°F (190°C).
In a skillet, heat olive oil over medium heat. Add peas and carrots, sautéing for 2-3 minutes until tender.
In a large bowl, combine shredded turkey, cranberry sauce, Dijon mustard, sautéed vegetables, and thyme. Mix well to combine.
Roll out the pie crusts on a floured surface. Use a round cutter to cut circles suitable for your muffin tin.
Press the pie crust circles gently into the muffin tin, making sure to cover the sides.
Fill each crust with the turkey mixture until almost full.
Roll out additional pie crusts for lids and cut out circles again; place on top of the filled pies, pressing to seal the edges.
Brush the tops with the beaten egg to achieve a golden color.
Bake for 20-25 minutes or until the tops are golden brown.
Allow the mini pies to cool slightly before removing them from the tin.