1. Make filling: Warm oil in a large skillet over medium-high heat. Add onion, celery and bell pepper and cook, stirring often, until softened, about 7 minutes. Add flour and stir for 1 minute. Pour in broth and bring to a boil, scraping browned bits from bottom of skillet, until mixture is thick and creamy.
2. Reduce heat to medium-low and stir in milk. Add chicken and cook, stirring, until firm and opaque, about 7 minutes. Stir in peas and carrots. Season with salt and pepper. Pour into a 2-quart baking dish.
3. Make topping: Preheat oven to 425°F. In a food processor, pulse flour, baking powder and salt. Add butter and pulse until mixture resembles coarse meal. With processor on, add oil and 1 cup milk. Process just until dough forms a ball. Turn out onto floured work surface; knead for 10 seconds. Roll dough to 1/2-inch thickness. Use a 2-inch cookie cutter to form 16 biscuits. Place biscuits on top of filling and brush with remaining milk.
4. Bake pot pie until filling is bubbling and biscuits are lightly browned on top, about 25 minutes. Serve hot.