Melt the butter in a large skillet over medium-high heat, then add the onion, carrots and celery. Cook, stirring the vegetables around, until they start to soften,. Chicken pot pie is the ultimate comfort food, so we sought a way to streamline this classic dish and make individual pot pies that we could pull out of the freezer. This is my offering for this year's pi day: individual chicken pot pies. This recipe has all the good stuff: chicken thigh meat, carrots, celery.