Add the trivet to the Instant Pot and pour in 1 cup of water. Set the potatoes on top of the trivet (it's okay if some fall to the wayside into the water). Secure the lid, move the valve to the sealing position, and hit Manual or Pressure Cook on High Pressure for 8 minutes. Quick release when done.
Using oven mitts, remove the liner and carefully pour the contents into a colander. Return the liner pot to the Instant Pot and add the potatoes back in. Using a potato masher, mash the potatoes right in the pot. Mash until most of the big chunks are gone.
Hit Cancel followed by Sauté and Adjust so it's on the Less or Low setting. Add the butter and mix in with the potatoes. Then, pour in the heavy cream and stir until combined.
In a couple of batches, add all the shredded cheese and stir in using a silicone spoon (NOTE: silicone coated utensils work best with melty cheese as it won't stick as much). Keep stirring constantly and, like magic, you'll see the potatoes begin to take on a stretchy, taffy-like consistency and officially become aligot.
As you mix, continue to taste and season with salt and pepper as needed. Keep stirring until it gets nice and hot and super creamy (about 5 minutes). When done, hit Cancel button followed by the Keep Warm button. Leave the aligot in the pot while serving as the heat is essential to keep that cheesy stretch going; transferring it to a serving dish will cause it to firm up if left at room temperature for too long. To that point, once plated, enjoy sooner rather than later for best results.
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