Melt the butter in a large pot over medium heat. Add the onions, celery, and carrots, and sauté until the onions are soft and translucent.
Add the diced potatoes to the pot, and stir to combine with the vegetables.
Pour in the fish stock and bring to a boil. Reduce the heat and simmer until the potatoes are tender, about 15 minutes.
Add the fish fillets to the pot and continue to simmer until the fish is cooked through and flakes easily with a fork, about 10 minutes.
Stir in the heavy cream, and season with salt and pepper to taste. Cook for an additional 5 minutes to warm through.
Serve hot, garnished with fresh dill if desired.