2 sheets (1 box) puff pastry, thawed according to package instructions
1 egg, beaten and mixed with 1 Tablespoon water
Kosher salt & fresh ground pepper to taste
Preheat oven to 350 degrees F. Place chicken breasts on a baking sheet lined with parchment paper. Season chicken breasts with salt and pepper and drizzle with olive oil. Bake chicken in preheated oven for 30 minutes or until chicken skin is golden brown. Allow chicken to cool.
Once chicken has cooled, remove skin and discard. Cut or pull chicken from the bones. Discard the bones and dice the meat into bite-size pieces. You should have about 1.5 to 2 cups of chicken.
In a large pot or Dutch oven, melt butter over medium heat. Add onion and carrots and cook until onions are translucent and carrots are soft, about 5 minutes. Add flour and cook for about 2 minutes more.
Slowly add chicken broth, stirring continuously to create a smooth sauce. Cook over medium heat about 10 minutes, until sauce has thickened.
Remove from heat and add half & half, mixed vegetables, chicken and parsley. Season mixture to taste.
To assemble pies, unroll puff pastry and use a biscuit cutter to cut 16 discs sized to fill each cocotte. Place a piece of pastry in the bottom of each cocotte. Pour in filling until each cocotte is about ¾ full. Top with a second piece of puff pastry.
Brush each pie with egg wash and sprinkle with salt & pepper. Place cocottes on a rimmed baking sheet. Bake in a 375 degree F oven until pastry is golden and filling is bubbling, about 30 minutes. Remove from oven and transfer cocottes to wire racks to cool slightly.
Serve immediately or cover and refrigerate for up to 2 days.