While potatoes are cooking, sauté cabbage and leeks in a skillet with butter until tender. Add garlic, and cook for 1 minute. Stir in half and half, bring to a simmer, and remove from heat.
Stir vegetable mixture into the cooked potatoes. Use a potato masher to fully combine and mash to desired consistency. Season to taste with salt and pepper.
Mound potatoes into a serving bowl. Make a shallow well in the center of the potatoes. Drizzle with melted butter, garnish with snipped chives, and serve.