Peel potatoes and cut into cubes; slice the leeks (the white and green parts). Set aside.
Bring chicken broth, potatoes, leeks, and chopped garlic to a boil. Reduce heat to medium-low, cover, and cook 15 minutes or until potatoes are tender.
Puree mixture in a blender or food processor, working in batches. Return pureed mixture to the saucepan and stir in milk, sour cream, salt, and pepper; continue to cook over medium heat until warmed through.
Top soup with Parmesan cheese, and serve sliced apples on the side.