Put the potatoes in a large pot and cover with cold water.
Bring to a boil and cook until the potatoes are very tender.
Meanwhile, heat the butter and half-and-half in a small saucepan over low heat.
Drain the potatoes and return to the pot. Mash up the potatoes a little with a potato masher. Add the melted butter mixture a little at a time and use the potato masher to combine. Once it has all been added, use a wooden spoon or spatula to give it a few stirs to combine completely. Stir in the salt and pepper and stir to combine. Serve immediately.
Half and half is a common dairy product sold in the U.S. If it's not available where you live, you can substitute half whole milk and half heavy cream.
You can keep these mashed potatoes warm in a slow cooker if making for a holiday dinner. Splash some cream on the bottom of the slow cooker, add the mashed potatoes, and then a splash of heavy cream on top. Keep the slow cooker on warm and stir occasionally. If the potatoes seem dry at any point, then just stir in some additional cream.
These are very well seasoned (there's nothing worse than bland mashed potatoes!); if you're watching your salt intake, you may want to cut back on the salt to start and then add more to taste.