Preheat your oven to 400°F (200°C).
In a skillet, melt butter over medium heat. Add flour and cook, stirring constantly, for 1-2 minutes.
Gradually whisk in chicken broth and heavy cream. Cook until thickened, about 5 minutes.
Add shredded chicken, peas, and carrots. Season with salt and pepper. Cook for another 5 minutes.
In a mixing bowl, combine flour, baking powder, and salt for the biscuit crust. Cut in cold butter until mixture resembles coarse crumbs. Stir in milk until just combined.
Pour chicken mixture into a baking dish. Drop biscuit dough by spoonfuls over the top.
Bake for 20-25 minutes, or until the biscuits are golden brown.