Step 1

Trim dark green leaves from leeks; discard all but Tuck thyme, rosemary, and bay leaves inside leek leaves; tie closed with kitchen twine. Thinly slice light and pale-green parts of leeks.

Step 2

Heat butter in a large heavy pot over medium-high. Add celery and sliced leeks and season with salt and pepper. Cook, stirring, until leeks begin to soften, about 5 minutes. Reduce heat to medium-low, add herb bundle, cover pot, and cook, checking and stirring occasionally, until leeks and celery are very soft, 25–30 minutes (this long, slow cooking draws maximum flavor out of the vegetables). Increase heat to medium-high, add potato and 5 cups broth, and bring to a boil. Reduce heat and simmer, stirring occasionally, until potato is very tender, 10–15 minutes. Let cool slightly. Discard herb bundle and any herbs that may have fallen out while cooking.

Step 3

Working in batches, purée leek mixture in a blender until very smooth (make sure lid is slightly ajar to let steam escape; cover with a towel). Transfer to a large bowl or pitcher.

Step 4

Pour soup back into pot and add cream. Thin with broth, if needed. Taste and season with salt and pepper; keep warm.

Step 5

Heat oil in a small skillet over medium. Add almonds, sunflower seeds, and coriander seeds and sprinkle sugar over; cook, stirring, until nuts and seeds are golden, about 4 minutes. Transfer nuts to paper towels to drain; season with salt and pepper.

Step 6

Serve soup topped with crème fraîche and nut mixture.

Step 7

Do ahead: Soup and nut mixture can be made 4 days ahead. Let soup cool; cover and chill. Store nut mixture airtight at room temperature.