Fill a large pot halfway with cold water. Peel the potatoes and cut into 2 inch cubes, adding to the pot as they are cut. Add cold water to cover by 1 inch, if needed. Stir in the 3 tbsp kosher salt.
Bring to a boil, then reduce heat to medium low and gently simmer until tender, 10-15 minutes. Drain potatoes and transfer to a baking sheet. Let dry 5-10 minutes.
Meanwhile, heat milk, cream, peppercorns, sprigs and bay leaves in a small saucepan over medium heat, stirring occasionally, until mixture is very hot but not boiling, about 10 minutes.
Remove from heat and let mixture infuse for 20 minutes then strain.
While milk mixture is infusing, pass the potatoes through the smallest disk of a food mill along with the diced butter into a large bowl. The hot cream mixture should be ready by this time so stir into the riced potatoes. Season with salt and pepper.
If you need to hold the mashed potatoes, cover with plastic wrap pressed directly against the potatoes surface and set bowl over a large pot of simmering water for up to 2 hours.