First, prep the ingredients. Cut the onion into chunks. Peel and cut the potatoes into chunks and put in a large bowl of cold water. Mince the garlic.
For the leeks, use only the white and light green parts. Discard the dark green part of the leek. Cut the leek into rings and then put into a bowl of water. Push the leek rings apart so any dirt that is caught in there can be removed. Then drain the water out and rinse the leeks one more time to make sure all dirt is removed.
Turn the Instant Pot onto SAUTE mode. Add the butter and let melt. Then add the onion and leeks and saute for 5-7 minutes, until leeks and onion are softened.
Add the garlic, herbs de Provence seasoning, and dried thyme leaves to the pot. Stir and saute for another minute.
Press the CANCEL button. Drain the potatoes and add them to the Instant Pot. Add the broth, salt, and pepper.
Close the lid and make sure valve is in the SEALING position. Push the Pressure Cooker (Manual Setting) button to high pressure and set the time to 6 minutes by using the + or - button.
Once Instant Pot is done, QUICK RELEASE the sealing valve. Let all the steam come out, and once the steam is completely done being released, you can open the lid. There will still be a bit of steam inside, so open the lid carefully.
Add the heavy cream and either use an Immersion Blender to blend the soup or blend in batches in a regular blender.
Serve in bowls and top with additional cream and chives if desired.
Notes
After peeling and dicing the potatoes, I put them in a bowl of cold water so that they don't oxidize and turn brown while I'm prepping and cooking the other ingredients.
If you don't have herbs de provence seasoning, you can instead use more dried thyme leaves and dried rosemary leaves.
If your leeks have a lot of dirt, I'd recommend slicing them lengthwise before cutting them into rings. That will help them come apart even more easily in the water and help any hidden dirt come out.