Boil the potatoes until fork tender. Drain in a colander and transfer back to the pot set over low heat. If you want to make sure the potatoes are super hot when served, warm the milk and melt the butter in a small pot. You can also just pour the milk straight into the potatoes, and add the butter in chunks.
Mash the potatoes, milk and butter together. When the mash is not quite yet to your desired consistency, add the parmesan and cheddar cheese, pepper, and salt. Continue mashing the potatoes to combine the cheese until melted.