Melt the butter in a medium saucepan. Once melted, add the water or fish stock.
Add peas, carrots, and potatoes to the saucepan.
Rinse the fish fillet and remove all bones. Cut into small pieces and add to the saucepan. Cook for 15–20 minutes. The fish should flake easily and the vegetables should be getting tender.
Add the milk, thyme, and parsley. Simmer for another 5–10 minutes. Either serve as a chunky soup, or purée in the food processor.