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.
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.
