Place the potatoes in a large pot, cover with cool water to a depth of 2 inches, and bring to a simmer over high heat. Reduce the heat and simmer until tender when pierced with a fork, about 25 minutes. Drain, then return potatoes to the pan and place over medium-low heat 1 to 2 minutes to dry potatoes, stirring occasionally.
Add the white chocolate to the still-hot potatoes; stir until the white chocolate starts to melt. Stir in the salt and hot red pepper sauce.
Use an electric mixer at medium-low speed to mash the potatoes slightly. Pour in the milk and continue mixing until creamy, about 1 minute. Serve at once.