Place the sliced potatoes in the Instant Pot. Pour over the broth, sprinkle in the garlic powder, salt, thyme, and pepper and stir to combine.
Cook on Manual High for 1 minute. Perform a quick release of the remaining pressure when the timer goes off. Press Cancel.
Use a slotted spoon to transfer half of the potatoes to a small oven-safe dish. Sprinkle half of the ham over the potatoes, then spoon the remaining potatoes over, leaving any broth behind.
Press Saute. Add the cream to the pot and bring it to a simmer, then press Cancel and stir in 1 cup of cheese. Whisk until melted and combined. Stir in the remaining ham.
Pour the cheese sauce over the potatoes, gently tossing to combine. Sprinkle the rest of the cheese over the top.
Bake for 15 minutes until bubbly, then broil on high for 2-3 minutes until the top is golden brown.