Warm the olive oil in a soup pot or Dutch oven over medium heat. Add the leeks and cook for about 5 minutes until tender. Stir in the garlic, salt, and pepper, and cook for an additional minute.
Add the fennel, potatoes, and vegetable broth to the pot. Increase the heat to bring to a boil, then reduce heat to maintain a simmer. Cover and cook for 20 to 25 minutes until the potatoes are fork-tender.
Remove the soup from heat. Use an immersion (handheld) blender to puree the soup right in the pot. See notes for instructions on using an upright blender.
Stir most of the heavy cream into the soup, reserving a few tablespoons to drizzle on each bowl of soup.
Ladle the soup into bowls, top with a drizzle of cream, and sprinkle with chopped chives. If your fennel bulbs came with their fronds, feel free to use those as a topping too. Enjoy!
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Upright blender instructions: Transfer the soup in batches to an upright blender. Do not fill all the way to the top. Leave a corner of the lid cracked to let steam escape. Blend until smooth, transfer the blended soup to a large bowl, and repeat with the rest of the soup until it's all blended.
Other toppings: chopped bacon, croutons, scallions.
Storage and freezing: Leftovers will keep in an airtight container in the fridge for 5 days. To freeze the soup, let it cool completely before transferring to containers. Leave about an inch of headspace to accommodate the soup expanding while freezing. You can reheat the soup directly from frozen in a saucepan with a lid, stirring frequently to prevent scorching. Or you can thaw it overnight in the fridge before reheating.