Slice potatoes into 1/4-inch thick slices using a mandolin. Rinse under cold water to remove excess starch.

Turn on a multi-functional pressure cooker (such as Instant Pot). Add potatoes, chicken broth, onion, parsley, garlic powder, paprika, salt, and pepper. Close and lock the lid. Select high pressure according to manufacturer's instructions; set timer for 1 minute. Allow 10 minutes for pressure to build.

Release pressure carefully using the quick-release method according to manufacturer's instructions, about 5 minutes. Unlock and remove the lid.

Add evaporated milk, Cheddar cheese, and Monterey Jack cheese to the pot. Gently stir until cheese is melted. Transfer potatoes to an oven-safe baking dish.

Set an oven rack about 6 inches from the heat source and preheat the oven's broiler to low. Broil for 4 minutes or until top is brown and bubbly. Remove potatoes from the oven and let rest for 10 minutes to thicken.