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Heat a large Dutch oven over medium heat. Add butter.
Add leeks and cook until tender, about 8-10 minutes.
Add garlic and cook until fragrant, about 30 seconds.
Add wine and cook until wine has mostly cooked off, about 2-3 minutes.
Add broth, potatoes, salt, and pepper, and bring to a boil. Reduce to a simmer, and simmer partially covered, stirring occasionally, until potatoes are tender, about 15-20 minutes.
Using an immersion blender, blend the soup until only a few chunks of potato and leek remain.
Add cream and nutmeg and stir. Let simmer, stirring occasionally, until thickened, 10-15 minutes.
Add shredded cheese and stir until melted. Adjust salt and pepper to taste.
Serve warm topped with chopped chives, if using.