Melt butter in a medium pot over medium heat. Add onion; cook and stir until softened, about 3 minutes. Add leeks; cook and stir another 5 minutes. Add potatoes and broth. Bring to boil, then reduce heat and simmer 20 minutes, or until potatoes are tender, stirring occasionally.
Blend in batches using a traditional blender (see recipe note #1) or use an immersion blender to reach your desired consistency (from slightly chunky to silky smooth).
Return soup to pot. Stir in milk or cream and season to taste with salt and freshly ground black pepper. Reheat if necessary.
Serve topped with chopped chives.
If you use a traditional blender (not an immersion blender), cover the top with a clean towel instead of the lid when blending anything hot - otherwise it will splatter out and could burn you and make a terrible mess.
Half and Half is a nice compromise between milk and cream if you happen to always have it on hand like I do (coffee!).