Chicken Pot Pie

INGREDIENTS

• 1 egg
• 1 large yellow onion
• 3 celery stalks
• 1 1/2 cups (3 sticks) cold butter
• 5 tablespoons cold water
• 1 teaspoon salt
• 1/2 recipe Thyme Pastry, recipe follows
• 3 cups all-purpose flour
• 1/4 cup all-purpose flour
• Black pepper
• 1 tablespoon distilled white vinegar
• 2 sprigs fresh thyme
• 1 sprig fresh thyme leaves
• 4 tablespoons (1/2 stick) butter
• 1 teaspoon kosher salt, or more as needed
• 1 chicken bouillon cube
• 1/2 cup frozen peas
• 1 cup heavy cream
• 1/4 cup white wine, optional
• 2 cups low-sodium chicken broth or stock
• 3 medium carrots, peeled
• One 2- to 3-pound chicken fryer, cut up