Working lightly, peel the parsnips and cut off the bottoms and tops. Continuing to use the vegetable peeler, cut away and save the rest of the parsnip down to its woody core, catching the thin slices in a wide soup pot. The color of the vegetable will change from creamy white to ivory when you get to the core. Discard the cores.
Add the butter, onion, potato and salt to the parsnip in the soup pot along with one-third to one-half cup of the water. Place the pot over low to medium-low heat, cover it tightly and cook slowly, "sweating" the vegetables until they begin to become tender, about 20 to 25 minutes. Stir from time to time to keep the vegetables from sticking and scorching.
Add the tarragon and parsley and continue to sweat the vegetables another 5 minutes. Add the remainder of the water, increase the heat to medium and cook uncovered until the vegetables are completely tender, about 15 minutes.
Remove the tarragon and parsley sprigs and, using a slotted spoon, transfer as much as you can of the solids from the soup pot into a blender. With the lid of the blender removed (cover the top with a paper towel), pulse the blender to chop the vegetables. If necessary, add a little water or cooking broth.
After the vegetables are chopped, turn the blender on the lowest speed and gradually work your way up to the highest. When you start pureeing the vegetables, they'll jump up the sides but then they'll subside and remain at much the same level no matter the speed of the blender. With the motor running, add the rest of the liquid and any vegetables left over and puree until completely smooth.
Wipe out the pot to remove any bits of vegetable and then pour the pureed soup back into it. Heat through over low heat and taste and correct the salt.
Beat the sour cream with a spoon to soften it.
Divide the soup among 4 warmed soup bowls and dribble in a bit of sour cream in a decorative pattern.