Wash the red potatoes and cut them into 2-inch chunks. Place them in a large pot (at least 5 quarts in size) and add enough cold water to cover the potatoes by about an inch.
Bring the potatoes to a boil over high heat. Once boiling, reduce the heat to medium-high and cook until a fork slides in and out of the potatoes easily with no resistance, about 15–20 minutes. Note: If the water starts bubbling over during cooking, lower the heat a little.
While the potatoes cook, warm the butter and garlic together over low heat in a small saucepan. Once melted, let the garlic butter sit on low heat until the potatoes are ready. Do not let the butter simmer.
Once the potatoes are done, drain them in a colander and then return them to the pot, off the heat. Pour the garlic butter over the top, then add the half-and-half, salt, and pepper.
Mash the potatoes with a potato masher (or an electric mixer) until they're as smooth as you like. At first, they may look a little soupy, but they’ll thicken up as you mash.
Taste the potatoes and adjust the seasoning with more salt and pepper if needed. Serve right away, or keep covered on low heat for up to an hour until ready to serve.