Heat oven to 400° F. Cook the chicken in a pot of simmering water until cooked through, 10 to 12 minutes; let cool, then shred.
Meanwhile, heat the oil in a saucepan over medium heat. Add the onions and carrots and cook, stirring, until they begin to soften, 6 to 8 minutes (do not let them darken). Sprinkle the flour over the vegetables and cook, stirring, for 1 minute.
Add the 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 teaspoon salt, and 1/4 teaspoon 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.
I like the recipe, but needs a few additions per other readers. Definitely needs more salt and more herbs as its a bit bland. I would use the recommendation of using the double crust next time as directly out of the oven its very hard to serve as there is nothing to contain the bottom. I did miss the richness that is usually expected as a comfort food, but if you think healthy its a solid second.
I like the lower fat in this recipe. Next time for more flavor I'd up the salt to 1 teaspoon, add Herbs d"Provence, and boullion to the stock. Using the meat from a rotisserie chicken makes it a bit easier to prepare.