Start by heating olive oil in a large skillet over medium heat. Add the onion, carrots, and celery, cooking until softened. Stir in the garlic and let it cook briefly until fragrant.
Sprinkle the flour over the vegetables and stir well so it coats everything evenly. Slowly pour in the chicken broth and milk, stirring constantly until the sauce thickens into a creamy base.
Mix in the cooked chicken, peas, salt, pepper, and thyme. Let the filling simmer gently for a few minutes so all the flavors come together.
Transfer the filling into a greased baking dish, spreading it evenly. Place the biscuits on top, spacing them slightly apart so they bake evenly.
Bake in a preheated oven at 375°F (190°C) until the biscuits are golden brown and the filling is bubbling. Let it rest for a few minutes before serving.