Turkey Biscuit Pie

Name: Turkey Biscuit Pie
Ingredients: Extra-virgin olive oil, for drizzling; 2 large onions (1 cut into wedges, 1 diced); 1 2 1/2-pound skin-on boneless turkey breast half; 3 thyme sprigs, plus 2 teaspoons chopped thyme; Kosher salt and freshly ground pepper; 4 tablespoons unsalted butter; 2 carrots, chopped; 2 stalks celery, chopped; 1 tablespoon whole-grain mustard; 1/4 cup all-purpose flour; 2 cups low-sodium turkey or chicken broth; 1/2 cup whole milk; 1 cup frozen peas; 1 1/2 cups all-purpose flour; 1/2 cup cornmeal; 2 tablespoons chopped fresh chives; 2 teaspoons baking powder; 2 teaspoons sugar; Kosher salt; 1/4 teaspoon baking soda; Freshly ground pepper; 6 tablespoons cold unsalted butter, cubed; 3/4 to 1 cup buttermilk