Make dough: Place flour and butter into freezer for 30 minutes before starting crust process. In a large food processor, pulse flour, baking powder, and salt until combined. Add butter and pulse until pea-sized and some slightly larger pieces form. With the machine running, add ice water into feed tube, 1 tablespoon at a time, until dough just come together and is moist but not wet and sticky (test by squeezing some with your fingers). Turn dough onto a lightly floured surface, form into 2 balls, and flatten into 2 discs (making sure there are no/minimal cracks). Cover with plastic wrap and refrigerate for at least 30 minutes. Cook chicken: Preheat oven to 400°. Grease a large baking dish with butter and grease one side of a large piece of parchment with butter. Season chicken all over with salt and pepper then place in baking dish. Place buttered side of parchment paper over chicken, so that chicken is completely covered. Bake until chicken is cooked through, 30 to 40 minutes. Let reset 10 minutes before cutting into cubes. Meanwhile, start filling: In a large pot over medium heat, melt butter. Add onions and carrots and cook until vegetables are beginning to soften, about 10 minutes. Stir in garlic, then stir in flour and cook until the flour mixture is golden and beginning to bubble. Gradually whisk in chicken broth. Bring mixture to a boil and cook until thickened, about 5 minutes. Stir in heavy cream, cubed chicken, peas, parsley and thyme. Season mixture with salt and pepper. Assemble pie: On a lightly floured surface, roll out one disc of dough into a large round about ¼” thick. Place in a shallow pie dish then add filling. Roll out second disc of dough into a large round about ¼” thick and place on top of filling. Trim and crimp edges, then use a paring knife to create slits on top. Brush with egg wash and sprinkle with flaky sea salt. Reduce heat to 375° and bake pie until crust is golden, about 45 minutes. Let cool for at least 15 minutes before serving.