01 - Melt the butter in a large pot over medium heat. Add the sliced leeks and sauté for 5–7 minutes until soft and translucent, taking care not to brown them.
02 - Stir in the minced garlic and cook for 1 minute until fragrant, being careful not to burn it.
03 - Add the diced Yukon Gold potatoes to the pot. Cook for 2 minutes, stirring occasionally to coat them in the butter and leek mixture.
04 - Pour in the vegetable stock and bring to a boil. Reduce heat to maintain a gentle simmer and cook uncovered for 20–25 minutes, until the potatoes are completely tender when pierced with a fork.
05 - Remove the pot from heat. Use an immersion blender to purée the soup until completely smooth, or leave some texture if you prefer a heartier consistency. If using a countertop blender, work in batches and exercise caution when blending hot liquids.
06 - Return the pot to low heat. Stir in the whole milk and grated Irish cheddar. Cook gently, stirring constantly, until the cheese is fully melted and the soup is heated through. Avoid boiling to prevent separating.
07 - Taste and adjust seasoning with sea salt, black pepper, and optional white pepper and nutmeg as desired. The soup should be well-seasoned but not overly salty since the cheddar adds its own salinity.
08 - Ladle the hot soup into warmed bowls. Garnish generously with additional grated Irish cheddar and fresh chopped chives. Serve immediately while hot.