In a large pot, bring salted water to a rolling boil. Carefully add the quartered red potatoes and cook until they are tender yet firm, which should take about 15 minutes. Drain the water from the potatoes.

Place the drained potatoes in a large mixing bowl. While they are still warm, add the unsalted butter, whole milk, and sour cream. Season with salt and black pepper to your liking.

Using a potato masher or an electric hand mixer, mash the potatoes until they reach your desired consistency. For a smoother texture, continue mashing or mixing until no lumps remain. For a chunkier texture, mash lightly.