Preheat the oven to 375°F. Remove the skin from the rotisserie chicken, pull the meat off the bone, and shred the chicken. Set the shredded chicken to the side.
In a large deep skillet, melt the butter over medium heat. Add the diced onion and sauté for 3-4 minutes. Then add the minced garlic and saute for another minute.
Sprinkle the flour in the skillet and stir together with the onions and butter. Continuously stir and cook the flour for about 1-2 minutes.
Turn the heat down to medium-low heat. Slowly add and stir in the chicken broth a little bit at a time. Continue stirring the broth until it is well combined with the flour. The roux will start to thicken as you stir.
Next, slowly stir in the milk along with the Italian seasoning, salt, and black pepper. Simmer the roux and continue stirring for 2 minutes.
Now add the frozen mixed vegetables and the shredded chicken to the skillet. Stir everything together and simmer for 4-5 minutes. After simmering, remove the skillet from the heat.
On a lightly floured surface, roll and stretch one pie crust until it is roughly 1-inch wider in diameter. This will serve as the bottom crust. Place the stretched pie crust in the bottom of a lightly buttered pie dish with the edges overlapping the dish (see photo above).
Add the chicken pot pie filling into the pie dish. Now roll and stretch the 2nd pie crust just a little, then add it on top of the filling. Fold and seal the edges of both pie crusts together (see photo above).
In a small bowl, combine a beaten egg and 1 tablespoon of water. Brush the egg wash over the top of the pie crust including the edges. Then cut slits into the top of the pie to allow steam to escape while it bakes.
Bake the pot pie in the oven for 35-40 minutes until golden brown. Once done, remove the pot pie and allow it to cool for at least 20 minutes before serving. Enjoy!