In a large pot, melt the butter over medium heat. Add the diced onion and leeks, and sauté until softened, about 5 minutes.
Stir in the minced garlic and cook for an additional 1 minute until fragrant.
Add the chopped potatoes and cabbage to the pot, stirring to combine with the onion and leeks.
Pour in the vegetable broth and bring the mixture to a boil. Reduce heat and let it simmer for about 20 minutes, or until the potatoes are tender.
Using an immersion blender, blend the soup until smooth. If you don’t have an immersion blender, carefully transfer the soup in batches to a countertop blender.
Once blended, stir in the whole milk, salt, pepper, and nutmeg. Heat through for another 5 minutes, then adjust seasoning to taste.
Serve hot, garnished with chopped fresh parsley.