For the buttermilk biscuits
1 cup all-purpose flour
1 cup cake flour
2 tsp baking powder
1/2 tsp baking soda
1 tsp granulated sugar
1/2 tsp table salt
4 tbsp (1/2 stick) unsalted butter chilled, cut into 1/4-inch cubes
3/4 cup plus 2 tbsp buttermilk
For the chicken pot pie filling:
1 1/2 tablespoons vegetable oil
1 large onion, chopped fine
3 medium carrots, peeled and cut crosswise 1/4-inch thick
2 small ribs celery, cut crosswise 1/4-inch thick
Kosher salt and freshly ground black pepper
4 tablespoons unsalted butter
1/2 cup unbleached all-purpose flour
1 1/2 cups milk
2 to 2 3/4 cups low-sodium chicken broth
1/2 teaspoon dried thyme
3 tablespoons dry sherry (optional)
3 to 4 cups (about 1 1/4 lbs) shredded chicken
3/4 cup frozen peas, thawed
3 tablespoons minced fresh parsley leaves