Arrange the chicken breasts in a single layer in the bottom of a 5-quart or larger crock pot. Sprinkle with ¼ teaspoon salt and ¼ teaspoon black pepper.
In a large skillet or Dutch oven, heat the oil over medium. Add the onion, mushrooms, celery, garlic powder, remaining ¾ teaspoon salt, and ¼ teaspoon pepper. Sauté until the onions soften and the mushrooms begin to brown, about 6 to 8 minutes. Stir in the thyme and sage. Transfer to the slow cooker.
Add the broth. Cover and cook until chicken is cooked through and reaches 165°, 1 ½ to 2 ½ hours on high or 3 to 4 hours on low.
Remove chicken from the slow cooker. Chop or shred and set aside.
Place the milk and butter in a large, microwave-safe liquid measuring cup or mixing bowl. Heat in the microwave until the butter melts. Whisk in the cornstarch, then pour the liquid into the slow cooker.
Stir in the chicken. Cover and cook on high for an additional 30 minutes to thicken. Stir in the frozen vegetables. Cover and cook for 10 additional minutes to warm through.
While the pot pie finishes cooking, preheat the oven and bake the biscuits according to the directions.
To serve, spoon the filling into serving bowls. Top with a hot biscuit and chopped parsley or thyme as desired. Enjoy immediately.
