01 - Melt the butter in a large pot over medium heat. Add the leeks and onion, and cook for 6–8 minutes, stirring occasionally, until soft but not browned.
02 - Add the garlic and cook for 1 more minute until fragrant.
03 - Stir in the potatoes, salt, black pepper, and white pepper.
04 - Pour in the vegetable broth, bring to a boil, then reduce heat and simmer uncovered for 20–25 minutes, until potatoes are tender.
05 - Remove from heat. Using an immersion blender, blend the soup until smooth, or leave slightly chunky if desired.
06 - Stir in the heavy cream and half of the grated cheddar. Warm gently over low heat until the cheese melts.
07 - Taste and adjust seasoning if necessary. Ladle into bowls, sprinkle with the remaining cheddar and chopped chives.