8 tablespoons unsalted butter, room temperature
4 ounces cream cheese, room temperature
1/4 cup heavy cream
1 1/2 cups all-purpose flour plus 2 tablespoons, plus more for rolling out the dough
1/2 teaspoon coarse salt

1 heaping cup of cooked, shredded chicken
2 tablespoons unsalted butter
1/2 cup chopped onion
1/3 cup chopped celery (1 large stalk)
1/3 cup chopped carrot (1 carrot)
1/2 teaspoon coarse salt
2 tablespoons all-purpose flour
1 1/2 cups chicken broth
1/4 cup grated Parmesan cheese
1 large egg, for egg wash

Process the butter, cream cheese, and cream in a food processor, electric mixer, or by hand to thoroughly combine. Add the flour and salt. Process just until combined and the dough holds together in a ball. Turn the dough out onto a well-floured surface. Divide into 2 pieces. Flatten into disks and wrap each in plastic wrap. Refrigerate for at least 30 minutes before rolling out. If the dough is chilled overnight, take it out 15 minutes before rolling out. Rub flour all over a rolling pin. Working with one dough disk at a time, place the disk on a clean, well-floured surface. Applying some pressure with the rolling pin, roll gently from the center of the dough to the top and bottom edges. Rotate the disk and roll to the top and bottom edges again. Reflour the work surface and rolling pin, turn the dough over, and continue to roll the dough from the center out to the edges. Turn over and roll again, rotating the disk to ensure even rolling until the dough is about 12 inches in diameter, thin but not transparent. To make the filling, melt the butter in a medium-sized hot skillet and add the onion, celery, and carrot. Saute over medium heat for 2 to 3 minutes. Stir in the salt and flour and cook for 1 minute more. Add the chicken broth and stir until thickened, about 2 minutes. Stir in 1 heaping cup shredded chicken and the Parmesan cheese. Cool in the fridge. Preheat the oven to 375 degrees. Butter or line a baking sheet. To form the pocket pies, work with half of a disk of dough at a time, rolling it out on a floured surface. Using an overturned bowl (about 5 inches across), cut out circles about 3 at a time from each piece of dough. After cutting out all your circles, gather all dough scraps, reroll, and cut out a final time. Place 1/4 cup filling on one side of a dough circle. Wet the edges of the dough with the water. Fold the dough over to form a half circle. Pinch the edge of the dough together. Crimp the edge with a fork. Repeat the process until all the filling is used. The pocket pies can be frozen at this point. Place the pocket pies on the prepared baking sheet and chill for a few minutes. Prick each pie on top twice with a fork. When ready to bake, beat the egg with 1 tablespoon water. Brush the egg wash over each pocket pie. Bake for 20 to 25 minutes, until golden brown. Let rest for 5 minutes before serving. The pies can be cooled and frozen to reheat in the microwave.