Bring a large pot of heavily salted water to a boil. Add the peeled and cut purple potatoes and cover with a lid. Let boil for 15 minutes.
In a separate pot over low heat, melt the butter with the half and half and garlic cloves. Don't let it boil.
Strain the potatoes and transfer to a bowl. Use a mixer on low speed or a potato masher to mash the potatoes. Remove the garlic from the melted butter and slowly stir the mixture into the potatoes. Season with salt and pepper and top with extra melted butter.
The waxier purple potatoes need more liquid to stay moist. You may still need extra half and half.