Peel and roughly chop the potatoes into quarters (if potatoes are especially large cut them into 2-inch pieces).
Place potatoes in a salad spinner or a colander set inside a large bowl. Fill with water to cover the potatoes by 1 inch and let soak 30 minutes. (Covered potatoes can be refrigerated for up to 4 hours.)
Meanwhile, combine the butter, leeks, and chives in a small saucepan and place over medium heat. When the butter has melted and it starts to bubble, reduce the heat to low and simmer until the butter is flavorful but the solids have not browned, 10 minutes. Remove from the heat and let steep for 20 minutes. Strain through a fine sieve and set the butter aside. (The solids can be reserved for stirring into the final dish or for another use.)
Remove the potatoes from the water and drain, being careful not to stir up the starch that has settled on the bottom. Move the potatoes to a large pot and cover with fresh water by 1 inch. Add 3 tablespoons of the salt and place over high heat until water comes to a gentle boil. Reduce the heat to medium to maintain a gentle but not full or “roiling” boil. Cook the potatoes gently until the internal temperature of the potatoes reaches 205 degrees and the thermometer probe meets barely any resistance, 25 to 35 minutes
Drain the potatoes then rinse thoroughly with hot water and allow to drain again.
Meanwhile heat the cream in the microwave for 45 seconds. Avoid boiling.
Return the potatoes to the pot and stir over low heat for 1 minute to dry them further. Add the melted butter then roughly mash the potatoes with a potato masher, being sure to press the masher all the way to the bottom of the pot. Add the warmed cream, white pepper and remaining tablespoon of salt.
Whip the potatoes with an electric hand mixer, starting on low then boosting the speed to high for 30 seconds. Scrape the sides of the bowl and whip for 10 more seconds. That's it. Whipping any further will result in gluey...not fluffy. Transfer to a large (ideally warmed) bowl and serve to a grateful world.