In a heavy-bottomed soup pot with lid (I use Le Creuset), melt the butter very slowly over low heat. Add the onion, stir to combine, and cover. Sweat the onion for about ten minutes, or until the onion is softened. Check every 5 minutes or so to make sure that the onion isn't cooking too quickly or browning

When the onions are softened, add the potato and carrots, and stir to combine. Add a very generous pinch of salt and stir again. Cover and sweat for another 10-12 minutes, or until you see a bit of liquid (not much) on bottom of the pot. As with the onions, check every 5 minutes or so to make sure that they aren't cooking too quickly or browning

Remove the cover, and add the stock (make sure that it is enough to cover), parsley, thyme, bay leaf, and a couple of twists of black pepper. Add the lemon juice. Raise the heat to medium

Stir, and taste. You'll very likely need to add more salt (I usually have 2-3 good pinches total in this recipe)

Bring to a boil, and then reduce the heat to keep the soup at a simmer

Skim the foam off the top. You don't need to do this perfectly, but it will improve the flavor of the soup

Continue to cook until the carrots and potatoes are very soft (you will need to be able to purée the soup). If the liquid gets significantly lower, add a little more stock or water and adjust seasoning. Remove from heat

Add the dill sprigs (remembering to save a couple for garnish) and stir. Taste and adjust for salt and pepper, if necessary. Blend the soup, using an immersion blender, until smooth

To serve, return the soup to a simmer. Serve garnished with cream, crème fraîche, or pats of butter (if desired), and a small sprig of dill