Preheat your oven to 400°F (200°C).
In a large skillet, sauté onions, carrots, and potatoes until they begin to soften, about 5-7 minutes.
Add the shredded chicken, peas, flour, thyme, salt, and pepper to the skillet, stirring well.
Pour in the chicken broth and milk, stirring until the mixture thickens, about 3-5 minutes.
Transfer the mixture to a greased baking dish, spreading it evenly.
In a bowl, mix the biscuit mix, additional milk, and melted butter until just combined.
Drop spoonfuls of biscuit dough over the chicken mixture, covering it in a somewhat even layer.
Bake for 25-30 minutes, or until the biscuits are golden brown and the filling is bubbling.
Let cool for a few minutes before serving.
