Peel the potatoes and put them in a large pot. Cover with water and white wine and bring to a boil. Cook until the potatoes are just past al dente, about 25 minutes.
Strain the potatoes and transfer them to a large bowl. Meanwhile, heat the butter, garlic, and half and half in a small sauce pot until it is at a simmer. Remove the garlic cloves and set aside.
Use a potato masher or a mixer on low to mash the potatoes. Add in the goat cheese, sour cream and stir until just combined. Slowly drizzle in the butter mixture while whipping the potatoes with a paddle attachment or rubber spatula.
Season with salt and pepper and serve with fresh minced chives on top.