01 - In a large pot, melt the butter over medium heat. Add the leeks and sauté for 5–7 minutes until soft but not browned.
02 - Stir in the garlic and cook for 1 minute until fragrant.
03 - Add the diced potatoes and cook for another 2 minutes, stirring occasionally.
04 - Pour in the vegetable stock. Bring to a boil, then reduce heat and simmer uncovered for 20–25 minutes, until the potatoes are tender.
05 - Remove the pot from heat. Use an immersion blender to blend the soup until smooth, or leave some texture if preferred. (Alternatively, blend in batches in a countertop blender—use caution with hot liquids.)
06 - Return the pot to low heat. Stir in the milk and grated cheddar. Cook gently, stirring, until the cheese is melted and the soup is heated through. Do not boil.
07 - Season with salt, black pepper, and optional white pepper and nutmeg to taste. Ladle into bowls. Garnish with extra cheddar and chopped chives.