Heat the butter in a 6- to 8-quart heavy-duty pot over medium heat. Add the onion, 1/2 tsp. salt, and a couple of grinds of pepper and cook, stirring occasionally, until the onion is soft and lightly browned, 8 to 10 minutes. Add the broth, leeks, parsnips, and potatoes and raise the heat to medium high. Simmer briskly for 5 minutes and then reduce the heat to low. Add the turmeric and cayenne, stirring well, and simmer slowly until the vegetables are very soft, about 20 minutes.
Working in batches, purée the soup in a blender and then strain it through a medium-mesh sieve. The soup should be about as thick as a thin milk shake; add more broth if it’s not thin enough. Return the soup to the pot and season to taste with salt. (The soup can be made up to this point 1 day ahead and refrigerated. Reheat before proceeding.)
Shortly before serving, heat the olive oil in a small skillet over medium-high heat. When the oil is hot, add the garlic, cumin seed, and mustard seed. Stir with a wooden spoon until the seeds begin to pop and the garlic is lightly browned, 30 to 60 seconds. Carefully stir the hot oil and spices into the soup (it may spatter). Season to taste with more salt, pepper, or cayenne.