In a large Dutch oven, heat 3 tablespoons (45g) butter over medium-high heat until melted. Add 3 tablespoons (24g) flour and cook, stirring constantly, until pale golden brown, about 3 minutes. Slowly whisk in broth. Add gravy, if using, along with onions, carrots, and celery. Bring to a simmer and cook, stirring occasionally, until vegetables are softened, about 10 minutes. Stir in turkey, peas, and half of parsley, and season to taste with pepper and 1 ½ teaspoons salt. Remove from heat.
Melt remaining 3 tablespoons (45g) butter. In a medium bowl, stir together remaining 1 ½ cups (192g) flour, baking powder, chives, remaining parsley, and remaining ¾ teaspoon salt. In a second bowl, whisk together buttermilk, egg, and melted butter in a second bowl. Pour buttermilk mixture over flour mixture and stir with a wooden spoon until it forms a shaggy dough.
Return stew to a bare simmer. Using a tablespoon measure, drop dumpling dough in 1-inch balls over surface of stew. Cover and cook until dumplings have puffed, feel firm to the touch, and a toothpick inserted in center of one comes out clean, about 15 minutes. Serve immediately.
