Preheat the oven to 450°F.
In a medium saucepan, melt butter over medium heat. Add diced onions and saute until onion is translucent (3 to 4 minutes).
Add flour, salt, and pepper. Cook, stirring constantly, until the flour mixture begins to brown (3 to 4 minutes).
Slowly stir or whisk chicken broth and whole milk into the flour mixture. Stir constantly while pouring just a bit at a time to make a smooth mixture.
Continue cooking over medium heat, stirring constantly to ensure milk does not burn on the bottom of the pan. Cook until mixture begins to bubble and thicken slightly (about 5 minutes). Remove from heat.
Stir in cream cheese, frozen vegetables, and diced chicken. Stir to mix evenly.
Prepare pie crusts by removing pie crust from packaging. Unroll one crust on a lightly floured surface. It is important to keep the crusts thick enough to hold the pie filling, so I did not roll the crusts out any thinner than they came in the package. Use a bowl, placed upside down, to cut out two circles from the dough. Gently gather together the scraps, roll out just enough to cut two additional circles (you may even need to do one at a time).
Place three crust circles onto a baking sheet sprayed with non-stick cooking spray.
Place a scoop of filling into the center of the circle.
Use a fork to beat the egg yolk with water.
Brush a bit of the egg yolk wash around the edge of the circle to help the sides seal. Now, fold the pie crust in half to form a crescent shape. Press down (work from the outer edge in) and then crimp with your fingers or a fork to seal the edges. Brush the whole hand pie with the egg wash. Use a fork to poke a few holes in the top of the pies.
Bake for 10 to 12 minutes or until the pies are golden brown and the crust is crispy. The filling is already cooked so we’re really just cooking the crust here.