Heat butter and olive oil in Instant Pot using the saute setting. Add leeks and onions and cook for 10 minutes, or until very soft. Stir frequently and partially cover with lid to keep moisture.
Add potatoes, broth, and salt. Cover and lock lid in place. Cook on high pressure for 4 minutes. Allow to release pressure naturally for 10 minutes, then move pressure valve to finish releasing pressure.
Allow soup to cool slightly, about 10 minutes. Use an immersion blender or transfer to a regular blender and blend soup until smooth.
Add ¼ teaspoon white pepper, milk, and Greek yogurt. Taste and adjust salt and pepper to your tastes.
Serve bowls of soup warm, at room temperature, or slightly chilled garnished with chopped chives.