While potatoes are boiling, melt 4 tablespoons butter in a large skillet until foaming subsides. Add cabbage and 1 teaspoon each kosher salt and black pepper. Cook over medium-high heat, stirring frequently, until cabbage is just starting to brown, 5-8 minutes.
Add leeks and an additional 1/2 teaspoon of salt. Continue cooking, stirring often, until vegetables are tender, 5-8 minutes more. Add garlic, and cook for an additional minute. Stir in half and half, bring to a simmer, and remove from heat.
*Keep in mind that the potatoes may look loose when the half and half is first added, but will naturally thicken as you mash the mixture, and within about 5 minutes of standing. If you prefer your mashed potatoes stiffer, reduce liquid to 3/4 cup.
I love using Irish butter in these rich potatoes. I generally use unsalted in the potatoes themselves so I can better control the saltiness of the dish. I’ll often use salted butter in the melted drizzle on top for an extra-luscious finish.