Make-dough: Put flour and butter to freezer for 30minutes prior to beginning crust process. In a large food processor, pulse flour, baking powder, and salt until blended. Add butter and pulse until pea-sized and some marginally bigger pieces form. With the till dough just come together, machine running, 1 tbsp at a time, add ice water to feed, and can be moist but not wet and tacky (test by squeezing a pair together with your fingers).
Turn dough onto a lightly floured surface, shape into 2 balls, and flatten into 2 disks (ensuring that there are no/minimal cracks). Cover with plastic wrap and refrigerate for at least 30minutes.
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 1 side of parchment paper over chicken, in order that chicken is totally covered. Let reset 10 minutes before cutting into cubes.
Meanwhile, start filling: In a large pot over moderate heat, melt butter. Add carrots and onions and cook till vegetables are starting to soften, about 10 minutes. Stir in garlic, then stir in flour & cook until the flour mixture is golden and start to bubble. Bring mixture to a boil and cook until thickened, about 5minutes. Stir in heavy cream, peas, parsley, cubed-chicken, and thyme. Season mixture with salt & pepper.
Assemble-pie: On a lightly floured surface, roll one disk of dough into a large round about 1/4" thick. Put in a shallow pie dish then add filling. Roll out second disk of dough into a large round about 1/4" thick and place on top of filling. Trim and crimp edges, then use a paring knife to make 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 45minutes. Let cool for at least 15minutes prior to serving.