Place potatoes and tablespoon kosher salt in a large pot, cover with cold water and bring to a boil. Boil until tender, 15 to 20 minutes. Drain and return to pot. Add buttermilk, 2 tablespoons butter, and 1/2 teaspoon salt. Mash until only small chunks of potato remain.
Melt remaining 2 tablespoons butter in large non-stick skillet. Add leeks and remaining 1/2 teaspoon salt, and sauté until leeks are lightly browned, about 5 minutes. Add cabbage and cook covered until cabbage is wilted, about 3 minutes. Uncover and cook until liquid is evaporated and cabbage is tender, about 5 minutes.
Gently fold leek and cabbage mixture and black pepper into mashed potatoes. Season with additional salt and butter to taste.