Place the potatoes and 2 tablespoons salt in a large pot. Add enough water to cover the potatoes by at least 1 inch and bring to a boil over high heat, then reduce to a simmer until the potatoes are cooked through and fork tender, 20 to 30 minutes.
Meanwhile, heat the half-and-half, butter, garlic, 1 teaspoon salt and 1/2 teaspoon black pepper in a small saucepan over medium heat. Bring to a simmer, then turn off then heat and set aside.
Drain the potatoes and pass through a ricer into a large bowl. Remove the garlic from the half-and-half mixture. Stir the half-and-half mixture, cabbage, three-quarters of the green onions and salt and pepper to taste into the potatoes until combined. Top with the remaining green onions and extra pepper.