Place potatoes in a large pot and cover with 2 inches of water. Add 1 teaspoon salt to water and bring to a simmer. Simmer until potatoes are soft, about 20 minutes. Drain well, reserving about 1/2 cup cooking liquid.
Place potatoes back in pot or in a large bowl. Add butter and use a potato masher or potato ricer to mash until smooth.
Stir in mayonnaise, salt, and both peppers.
If too thick add some of the reserved cooking liquid or you can add milk, but warm it first.