For the smoked paprika butter: Combine the butter, paprika, salt and pepper in a bowl. Roll into a log, wrap in waxed paper or parchment and refrigerate until very cold.
For the mashed potatoes: Put the potatoes in a large pot, cover by 2 inches with cold water and add 2 tablespoons kosher salt. Bring to a boil and cook until fork-tender, about 35 minutes. Drain the potatoes, run through a food mill set over a large bowl and rice until very fine.
Combine the milk and heavy cream in a small saucepan and bring to a simmer over low heat.
Put the potatoes back in the pot, place the pot back over low heat and, using a wooden spatula, stir the potatoes to dry them out. Begin adding the cold paprika butter little by little, vigorously stirring with a wooden spoon until the butter is incorporated. (Adding the cold butter slowly will create an emulsion.) Slowly stir in the warm milk mixture bit by bit, and then switch to a whisk and whisk until light and fluffy. Fold in the chives and season with salt and pepper.