Melt the butter in a small soup pot or saucepan and add the onion, celery, thyme, and bay leaf. Give it a stir, leave for a minute or two, and then add the potatoes and half the parsley mixture. Season with the paprika and 1/2 teaspoon of salt. Cook over medium heat for 5 minutes or so, occasionally stirring.
Add the milk, stock, or water. Bring to a boil, then cover the pot and simmer until the potatoes are tender. Mash a few of them against the sides of the pan to give the soup body. At this point, enrich the soup with a little half-and-half or more milk, if desired. Taste for salt and also paprika, adding more if you want it to be smokier. Season with freshly ground pepper.
Lay the salmon in the soup, cover, and cook 5 minutes longer. Serve yourself a bowl and sprinkle with the remaining parsley mixture and an extra shot of pepper.
Reprinted with permission from ©What We Eat When We Eat Alone, by Deborah Madison and Patrick McFarlin, published by Gibbs Smith click for book review
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