Chicken and Vegetable Pot Pie

1 pound boneless, skinless chicken breasts
1 tbsp olive oil
1 cup onions, diced
1 cup carrots, sliced in rounds
1 cup celery stalks, sliced on diagonal
1 cup potatoes, diced
10 button mushrooms, cut in chunks
1/2 cup all-purpose flour
1 cup dry white wine
2 cups 1 percent milk
1 10-oz package of frozen peas
1 tsp fresh thyme
Kosher salt and black pepper
1 package puff pastry, thawed if frozen (you can use phyllo, pie crust or biscuits also)

> Heat oven to 400. Cook the chicken in a pot of simmering water until cooked through, 10 to 12 minutes; let cool, then shred.

> Heat the oil in a saucepan over medium heat. Add the onions, carrots, and celery and cook, stirring, until they begin to soften, 6 to 8 minutes (do not let them darken). Add mushrooms and cook 2 to 3 minutes. Sprinkle the flour over the vegetables and cook, stirring for 1 minute.

> Add the white wine and cook until evaporated, about 5 minutes. Add the milk and simmer until the sauce thickens, 2 to 3 minutes. Stir in the chicken, peas, thyme, 3/4 tsp salt, and 1/4 tsp pepper. Transfer to a shallow 1 1/2 to 2 quart baking dish.

> Lay the crust on top, pressing to seal. Cut several vents in the crust. Place the pot pie on a baking sheet and bake until bubbling and the crust is golden, 30 to 35 minutes.