Melt the butter in a large pot over low heat. Once melted, add the chopped celery and carrots. Cook for approximately 5 minutes until the vegetables begin to soften.

Stir in 1/4 cup of flour to coat the vegetables evenly. Gradually pour in 1 cup of chicken stock, whisking constantly to ensure a smooth mixture.

Add the remaining chicken stock and the chopped potatoes to the pot. Increase the heat to medium-high and bring the mixture to a gentle simmer. Cook for 30–40 minutes, or until the potatoes are fork-tender.

While the soup is simmering, combine the flour, eggs, milk, and salt in a mixing bowl. Stir until a dough forms. Divide the dough into two portions, roll each portion into a log approximately 1 inch in diameter, and cut into 1-inch pieces to form dumplings.

Once the potatoes are tender, carefully drop the dumplings into the soup. Stir gently to ensure they do not stick together. Allow the dumplings to cook for about 5 minutes.

Remove the pot from heat and stir in the heavy whipping cream. Adjust the seasoning with additional salt if needed.

Ladle the soup into bowls and serve immediately. Optional garnishes include fresh parsley or a slice of crusty bread on the side.