Remove the skin from the salmon and place the skins into a large pot with about 5 cups of water. Bring to a gentle boil over medium-high heat, then simmer for 10 minutes. Discard the skins and reserve the stock.

Melt 2 tablespoons of unsalted butter in the same pot over medium heat. Add chopped leeks and a pinch of kosher salt. Sauté for 3-4 minutes until softened. Add white pepper and ground allspice, cooking briefly.

Add chopped potatoes and sliced carrots to the pot with the reserved fish stock. Bring to a rolling boil, then reduce to a low simmer. Cover and let tenderize for about 10-15 minutes.

Once the vegetables are tender, lower the heat and stir in 1 cup of heavy whipping cream along with the salmon chunks. Gently fold them into the soup and cook for 2-4 minutes until salmon is opaque.

Taste the soup and adjust seasoning with additional salt and pepper as needed. Serve piping hot, garnished with fresh dill.