Preheat a large ovenproof skillet to medium heat with the butter. Preheat the oven to 400F.
Add the carrots, celery, and onion to the skillet with some salt and pepper. Stir for about 5 minutes to soften, then sprinkle the flour over the veggie mixture. Stir to coat the veggies in the flour.
Slowly stream in the stock, stirring as you go, to incorporate with the floured veggies. Let the mixture come to a boil to thicken.
Add the cream, peas, and chicken to the chicken pot pie sauce. Taste, and add more salt and pepper to your preference. It should taste really good at this point!
Scatter the tater tots over the chicken pot pie filling. Sprinkle with salt and pepper if desired. Bake the chicken pot pie with tater tots at 400F for 30 minutes until the top is golden brown.
Let the chicken pot pie with tater tots rest for about 5 minutes before scooping into bowls and eating. You will likely have no leftovers.