Add leeks, cauliflower, garlic, chicken broth, and cinnamon to Instant Pot. Season with salt and black pepper, to taste.
Add lid and lock into place. Switch vent to “Sealing” position and set the “Manual” setting on high before adjusting the cook time to 9 minutes. After a brief pause, the Instant Pot will automatically start building pressure.
When finished cooking, do a quick release (QR) to allow the pressure to escape. Unlock and carefully remove lid. Add goat cheese, cream cheese, and sharp cheddar to the container and stir until cheese is completely melted.
Blend mixture with immersion blender until smooth (or transfer to blender or food processor if you don’t have an immersion blender). Taste and adjust seasonings, as desired.