Crust: Combine 1/4 teaspoon thyme, 1 teaspoon salt, 1/4 teaspoon garlic powder, and 1 1/2 cups flour. Cut 1 cup butter flavored shortening into the flour mixture. Add 1/2 cup sour cream to flour mixture; mix until incorporated. Shape into ball and refrigerate for 30 minutes.
Filling: Sauté the onions in 2 teaspoons of butter. In a large pan combine 1/8 teaspoon thyme, pepper, 3 tablespoons flour, and 2 1/2 tablespoons butter. Heat the mixture until smooth and bubbly.
Combine the chicken broth, 1/2 cup sour cream, heavy cream, 1/2 teaspoon salt and 1/8 teaspoon garlic powder. Add to the flour mixture in the pan and cook over low-medium heat, stirring until heated and thickened. Add the carrots, peas, and diced chicken to mixture. Keep warm on low heat while rolling out dough.
Divide the dough into two equal pieces. Roll each out to form two piecrusts. Place one piecrust into a pie pan.
Pour the chicken mixture into the piecrust; top with the remaining piecrust to form the upper crust. Slit a few holes in the top crust to allow steam to escape.Garnish with cut out crust pieces if desired.
Bake the pie at 425 degrees for 35-40 minutes until crust is brown. Let the pie set for 15 minutes before serving. Garnish as desired.