Melt the butter in a 5-quart / 4.7 L Dutch oven or soup pot over medium heat. Add the sliced leeks and cook for 6 to 8 minutes, stirring often, until soft but not browned.

Add the diced potatoes, stock, salt, and white pepper. Bring to a boil, then reduce heat and simmer uncovered for 20 to 25 minutes, until the potatoes are fork-tender.

Remove the pot from the heat and let the soup cool for 10 minutes.

Stir the chopped cucumber and dill into the warm soup.

Working in batches, puree the soup in a blender until completely smooth, about 1 to 2 minutes per batch. You can also use an immersion blender directly in the pot.

For a silkier texture, pass the puree through a fine-mesh sieve into a large bowl, pressing with a spoon.

Stir in the heavy cream and lemon juice. Taste and adjust salt and pepper, keeping in mind the soup will taste milder once it's cold.

Cover and refrigerate for at least 4 hours, or overnight, until completely chilled.

Taste the chilled soup again and re-season if needed, since cold mutes salt and acidity.

Ladle into chilled bowls or mugs. Garnish with diced cucumber, extra dill fronds, and a drizzle of cream.