01 - Melt butter in a large pot over medium heat. Add leeks and onion, sauté for 6–8 minutes until softened but not browned.
02 - Stir in minced garlic and cook for 1 minute until fragrant.
03 - Add potatoes, vegetable broth, salt, pepper, thyme, and bay leaf. Bring to a boil, then reduce heat to simmer. Cover and cook for 20–25 minutes until potatoes are very tender.
04 - Remove and discard the bay leaf from the pot.
05 - Using an immersion blender, purée the soup directly in the pot until completely smooth. Alternatively, transfer to a blender in batches and return to the pot.
06 - Stir in whole milk and heavy cream. Heat gently over low heat without bringing to a boil.
07 - Gradually add grated sharp cheddar while stirring constantly until fully melted and incorporated. Adjust seasoning as needed.
08 - Ladle hot soup into bowls and garnish with extra cheddar and fresh chives or scallions.