How to Make It
Preheat oven to 400˚F.
To prepare filling, heat oil in a large saucepan over medium-high heat. Add onion, carrot, and celery; sauté 4 minutes. Add chicken, salt and pepper; sauté 3 minutes. Stir in flour; cook 1 minute, stirring constantly. Add thyme sprigs. Slowly pour stock into pan, stirring constantly; bring to a boil. Reduce heat to medium; simmer 8 minutes, stirring occasionally. Remove from heat. Discard thyme sprigs. Stir in peas, green onions, and chopped thyme. Pour filling in a 9-inch baking dish coated with cooking spray.
To prepare crust, weigh or lightly spoon 13/4 cups flour into dry measuring cups; level with a knife. Combine 13/4 cups flour and next 5 ingredients in the mixing bowl of a heavy-duty stand mixer with paddle attachment. With motor running at low speed, add butter 2 – 3 pieces at a time, beating until butter breaks up into pea-sized pieces. Stir in 1 egg yolk. Add enough ice-cold water, 1 Tbsp. at a time, until a moist dough forms, beating just until dough forms a ball. Roll dough out to 12-inch circle. Place dough over top of pie plate, folding edges and fluting, pressing edges into sides of pie plate to prevent them from sinking. Cut 3 to 5 slits in top of pastry to vent.
Whisk cream and remaining 1 egg yolk together; brush mixture over top of pastry. Bake at 400˚ for 25 – 30 minutes or until pastry is golden brown and cooked through.