Preheat oven to 400°F (200°C).
In a skillet, melt butter over medium heat. Add flour and cook, stirring constantly, for 1 minute.
Gradually whisk in chicken broth and milk. Cook until thickened, about 5 minutes.
Add shredded chicken, peas, carrots, salt, and pepper. Stir to combine.
Pour mixture into a baking dish.
In a mixing bowl, combine flour, baking powder, and salt for the biscuit crust. Cut in cold butter until mixture resembles coarse crumbs.
Add milk and stir until just combined. Drop spoonfuls of biscuit dough over the chicken mixture.
Bake for 20-25 minutes or until biscuits are golden brown.