Preheat oven to 425° F and cook puff pastry shells according to package directions.
Slice carrots in half lengthwise and boil in lightly salted water until fork tender. Drain carrots and dice. Set aside.
Melt 1/2 tablespoon of butter and 1/2 tablespoon of oil together in a pan over medium heat. Add mushrooms, season to taste with kosher salt and pepper, and cook for about 5 minutes, or until soft and slightly carmelized. Set aside.
Melt remaining butter in a dutch oven or heavy bottomed saucepan over medium-low heat.
Add flour and stir to make a roux. Cook mixture for 2-3 minutes, stirring continuously and making sure it doesn't brown.
Stir in dijon mustard.
Slowly add broth to pot, whisking to combine. Then add cream and milk, and keep stirring until sauce comes to a boil and thickens.
Add chicken, peas, carrots, and mushrooms and pan drippings to mixture and stir to combine.
Sample sauce and season to taste with kosher salt and pepper if necessary.
Remove circular "lids" from puff pastry shells, fill with chicken mixture, and top with lid. Serve alongside your favorite vegetables and enjoy!