How to Make It
Whisk together 1/2 cup of the stock and 6 tablespoons of the flour in a bowl until smooth. Combine stock mixture, chicken, water, salt, bay leaves, and remaining 3 1/2 cups stock in a pressure cooker. Seal pressure cooker lid, and bring to high pressure. Cook 8 minutes.
While chicken cooks, combine 1 teaspoon of the pepper and remaining 2 cups flour in a medium bowl. Cut butter into flour mixture with your fingers or a pastry cutter. Add buttermilk, and knead with your hands just until dough comes together. Turn dough out onto a work surface, and press into a 1/4-inch-thick disk or square. Cut dough into 1/2-inch squares.
Release pressure according to manufacturer’s instructions. Discard bay leaves. Transfer chicken breasts to a cutting board or bowl; cool slightly, about 15 minutes. Remove and discard chicken skin, and pick chicken meat from bones. Shred meat, and discard bones.
Return stock mixture in pressure cooker to a simmer over medium-high. Add dough squares; simmer just until cooked through, 6 to 8 minutes. Stir in shredded chicken, tarragon, lemon zest, and remaining 1/2 teaspoon pepper.