Add potato, garlic, thyme, butter, and chicken broth to the instant pot. Seal, and set on manual pressure for 8 minutes. Quick-release steam once cooking is complete.
Mix cornstarch with water to create a slurry. Pour this into the instant pot and stir.
Set instant pot to saute, add whole milk, heavy whipping cream, ham, and cheddar to the pot. Stir to combine. Bring to a boil, and stir often for 5 minutes.
Turn off the instant pot. Lightly mash potatoes to desired consistency.