Start by heating olive oil in a skillet over medium heat. Add cubed chicken and cook until golden brown and fully cooked. Remove it from the pan and set aside. This helps lock in moisture while building flavor in the pan for the vegetables.
In the same skillet, add onions and garlic, cooking until softened. Toss in carrots and celery, letting them cook until just tender. Add peas, thyme, and seasoning. Stir well before returning the chicken to the pan. This creates a flavorful, colorful filling base.
In a saucepan, melt butter, then whisk in flour. Let it cook briefly to remove the raw taste. Gradually add broth and milk, whisking constantly until smooth and thickened. Pour the sauce over the chicken and vegetable mixture, stirring until everything is coated in creamy goodness.
Mix flour, baking powder, and salt in a bowl. Cut in cold butter until the texture looks crumbly. Gently stir in milk until a soft dough forms. Be careful not to overmix—keeping the butter cold ensures a fluffy, tender crust.
Pour the filling into a baking dish. Drop spoonfuls of biscuit dough on top, covering most of the surface. Bake at 400°F (200°C) for 20–25 minutes until the crust is golden brown. Let it rest briefly before serving to allow the filling to settle.