1. To prepare crust, weigh or lightly spoon 6.75 ounces (about 1 1/2 cups) flour into dry measuring cups; level with a knife. Combine 6.75 ounces (about 1 1/2 cups) flour and 1/4 teaspoon salt in a large bowl; cut in 7 tablespoons butter with a pastry blender or 2 knives until mixture resembles coarse meal. Add 5 tablespoons ice water; stir just until moist. Press mixture gently into a 5-inch circle; cover with plastic wrap. Chill 15 minutes. Roll dough into a 12 x 8-inch rectangle on a lightly floured surface. Chill dough until ready to use.
2. Preheat oven to 400°.
3. To prepare filling, melt 2 teaspoons butter in a Dutch oven over meduim-high heat. Add carrot, onion, and thyme; cook 8 minutes or until vegetables are soft. Add broth and potato; bring to a boil. Cover and simmer 10 minutes. Combine flour and 1/3 cup water in a small bowl; stir with a whisk until smooth. Return potato mixture to a boil. Slowly drizzle flour mixture into potato mixture, stirring constantly. Cook 1 minute or until mixture thickens. Stir in chicken, peas, 1/2 teaspoon salt, and pepper. Spoon chicken mixture into an 11 x 7-inch glass or ceramic baking dish coated with cooking spray. Place dough on top of chicken mixture, pressing to edge of dish. Cut 4 slits in top of crust to allow steam to escape. Gently brush crust with milk. Bake at 400° for 50 minutes or until golden and bubbly. Let stand 10 minutes.