To prepare filling
preheat oven to 425°F. Heat 2 tsp olive oil in a large skillet or Dutch oven over medium heat. Add leeks and carrots, and cook, stirring, until the leeks soften, about 7 minutes. Add garlic and cook, stirring, 1 minute more.
Pour in wine and stir until most of the liquid has evaporated. Add flour and sage and cook, stirring constantly, until the flour starts to turn light brown, about 2 minutes. Stir in broth and bring to a simmer, stirring constantly, until the sauce thickens and the carrots are barely tender, about 5 minutes.
Add turkey (or chicken) and peas, and season, to taste, with salt and pepper. Transfer mixture to a deep 10-inch pie pan or 2-quart baking dish and set aside.
To mash potatoes and bake pie
Place potatoes in a large saucepan, and add enough cold, salted water to cover them. Bring to a boil over medium heat. Cook, partially covered, until the potatoes are tender, about 10 minutes. Drain and return the potatoes to the pan. Cover and shake the pan over low heat to dry the potatoes slightly, about 1 minute. Remove from heat.
Mash the potatoes with a potato masher or whip with an electric mixer, adding enough buttermilk to make a smooth puree. Season with salt and pepper. Stir in egg and 1 tbsp olive oil.
Spread the potatoes on top of the turkey mixture. With the back of a spoon, make decorative swirls. Set the dish on a baking sheet, and bake until the potatoes and filling are heated through and the top is golden brown, 25 to 30 minutes.
Use leftover roasted turkey or chicken. Or, to poach chicken breasts, place boneless, skinless chicken breasts in a medium skillet or saucepan. Add lightly salted water to cover and bring to a boil. Cover, reduce heat to low and simmer gently until chicken is cooked through and no longer pink in the middle, 10 to 12 minutes.
No buttermilk? Use buttermilk powder, prepared according to package directions. Or make “sour milk”: mix 1 tbsp lemon juice or vinegar to 1 cup milk.