In a large measuring cup, stir together the chicken broth, evaporated milk, heavy cream, garlic and onion until well combined.
Set a wire trivet in a 6-quart or larger Instant Pot and pour in the water.
Grease a 7-inch round casserole dish with cooking spray or butter. Layer the potatoes, both cheeses, and the milk mixture into the prepared baking dish, until all are used up. Cover loosely with foil and place in the Instant Pot. Lock the lid in place, making sure the valve is set to seal. Pressure cook on high for 10 minutes and then do a quick release.
Carefully open the lid and remove the dish from the Instant Pot. Uncover and place under the broiler until the top is golden brown. This step is optional. Garnish with chives before serving.