Prepare the crust: Pulse the flour, baking powder and salt in a food processor until combined. Add the butter, one piece at a time, pulsing until the mixture looks like coarse meal. Separate the egg; refrigerate the egg white. Beat the egg yolk and milk in a bowl, then add to the food processor, pulsing until the dough comes together. Turn out onto a lightly floured surface and gather into a ball. Flatten into a disk, wrap in plastic wrap and chill at least 1 hour.
Meanwhile, make the filling: Preheat the oven to 425 degrees F. Prick the potatoes with a fork and bake directly on the oven rack until tender, about 45 minutes. Cool slightly, then peel and break into small pieces.
Bring the chicken broth, carrots and thyme to a simmer in a small saucepan over medium heat and cook 2 minutes; cover and keep warm. Meanwhile, heat the olive oil in a large pot over medium heat. Add the onion and cook until soft, about 8 minutes. Sprinkle in the flour and stir until lightly toasted, about 3 minutes. Add the milk, celery, potato pieces and the warm broth mixture and simmer until thickened, about 15 minutes. Remove from the heat and stir in the chicken, yogurt, peas and parsley. Season with salt and pepper.
Transfer the filling to a 2-quart casserole dish. Roll out the dough on a lightly floured surface until about 1/2 inch thick and slightly larger than the dish. Beat the reserved egg white in a bowl; brush over the dough and season with salt and pepper. Press the dough against the sides of the dish. Place on a baking sheet and bake until the crust is golden brown, 20 to 25 minutes.