Start by removing the skin from the skin-on salmon fillet and discarding any pin bones. Cut the salmon into bite-sized chunks and set aside in a bowl.

In a large pot, melt 2 tablespoons of unsalted butter over medium heat. Add the sliced leeks and sauté for about 10 minutes until they become soft and translucent.

While the leeks are sautéing, bring 5 cups of water to a boil in a separate saucepan. Add the reserved salmon skin and simmer for approximately 10 minutes.

Carefully pour the strained broth into the pot with sautéed leeks, stirring gently to combine. Next, chop the russet potatoes and large carrot and add them along with half of the fresh dill.

Once the potatoes are tender, add the salmon pieces to the pot along with 1 cup of heavy cream and a sprinkle of allspice. Reduce the heat to low and simmer for a few more minutes.

Ladle the soup into bowls, garnishing with the remaining fresh dill. Serve hot.