Cut and discard the bottom dark green parts of the leeks. Slice the remaining parts lengthwise then cut into small pieces. Rinse them in a large bowl of water to remove any dirt.
Turn the Instant Pot to saute. Add the butter and chopped leeks. Add the chopped onion and minced garlic. Continue to saute until softened. Turn off the saute function.
Add the potatoes, broth, and herbes de provence. Cook on high pressure for 8 minutes. Once cooking time is complete, let the pressure release naturally.
Open the lid, add heavy cream, then blend together using an immersion blender. Garnish with chopped chives if desired.