Adjust oven rack to upper-middle position; heat to 425 degrees. Place potatoes on a foil-lined pan; bake 45 to 60 minutes, until tender. Peel when cool enough to handle.
Puree with salt and pepper in a food processor. With motor running, gradually add milks through feeder tube, then butter. Process until silken. (Can make up to 2 days ahead; store in an airtight container.) Reheat and serve.