Prepare leeks: Slice off the root and the tough green top. Slice leeks lengthwise. Turn leeks so that their flat sides are facing down. Slice leeks into thin half-moons.
Heat an enameled cast iron Dutch oven or other heavy soup pot over medium heat. Add olive oil, butter, and prepared leeks to the soup pot. Stirring almost constantly, sauté leeks until they wilt and become translucent; about 5 minutes.
Add minced garlic to leeks and continue sautéing until garlic is fragrant.Add diced celery and grated carrots to the leek mixture and cook, stirring frequently, for 3-5 minutes, until celery begins to look slightly translucent.
Add clam juice, vegetable stock, tomato paste, white wine, water, paprika, salt, pepper, lemon juice, and hot sauce.
Stir in all of the diced potatoes and bring mixture in pot to a boil. Reduce heat and simmer for 10-15 minutes, or until the diced potatoes are tender but not mushy. Remove from heat.
OPTIONAL: If you like your chowder extra creamy, use a potato masher to break up potatoes just a bit before moving on. Remember though, this is a chowder: you want it to be chunky!You can also use an immersion blender to break down the mixture, but don't get carried away.
Using your fingers (or a knife), flake the smoked salmon into small pieces. You want it to be roughly the same size and texture as flaked chunky canned tuna. Add ¾ of the salmon (6 ounces) to the soup mixture, reserving 2 ounces to finish the soup.
Prepare Tarragon: Separate a few small springs of tarragon from the larger stem to use later for garnishing chowder. Set aside. Option 1: Remove a small handful tarragon leaves from the stem. Using the palm of your hand, roll the leaves on the counter or cutting board to bruise, and then coarsely chop. Add about 1 ½ - 2 tablespoons of chopped fresh tarragon to chowder mixture. Option 2: Leave tarragon on stem, and stir entire stem into chowder. If you choose to leave the tarragon stem whole, you can remove it just before serving, or leave it in the soup pot and work around it as your serve.
Add fresh tarragon and heavy cream to the leek mixture and give it a good stir.
Allow the chowder to steep in its own heat (i.e., off the stove) for at least a half an hour. This will give the smoky salmon and fresh tarragon flavors time to infuse themselves into the mixture. I usually make this chowder a day ahead of time, and let it rest overnight in the fridge.
When ready to serve, return the chowder to the stovetop and heat on low to bring it back up to temperature. DO NOT BOIL!
Serve in bowls: Finish chowder with a splash of heavy cream, a generous sprinkling of the reserve flaked smoked salmon, and a small sprig of fresh tarragon.
For this smoked salmon chowder recipe, you want to use hot-smoked salmon. Hot-smoked salmon is smoked basically like meat, resulting in a firm, flaky piece of fish. The flavor and texture will be similar to grilled salmon, with smoky undertones.