Prepare the potatoes: Peel (optional) and cut the Yukon Gold potatoes into even 1–1½ inch chunks so they cook at the same rate.
Salt the cooking water generously: Place potatoes in a large pot and add cold water to cover by about an inch. Add about 1 teaspoon kosher salt to the water and bring to a boil over high heat.
Cook until tender: Reduce to a simmer and cook the potatoes until a fork slides through easily, about 12–15 minutes depending on size.
Warm the milk and butter: While potatoes cook, gently heat the milk and butter together in a small saucepan until the butter is melted and the mixture is warm. If using garlic, lightly crush a clove and simmer briefly in the milk for a subtle infusion, then remove the garlic.
Drain and dry the potatoes: Drain the potatoes in a colander, then return them to the hot pot over low heat for 1 minute, shaking occasionally to evaporate excess moisture. This helps keep mashed potatoes fluffy, not watery.
Mash the potatoes: Use a potato ricer for the smoothest texture or a sturdy masher for a slightly more rustic feel. Press or mash until no large lumps remain.
Add cheeses and dairy: Stir in the mascarpone (or cream cheese) until incorporated. Then gradually add the warm milk-and-butter mixture a little at a time, mashing or stirring until you reach your desired consistency.
Fold in cheddar and Parmesan: Add the shredded sharp cheddar and grated Parmesan, mixing gently until melted and evenly combined. Taste and add salt and freshly ground black pepper as needed.
Finish and serve: Transfer to a warmed serving bowl, top with a pat of butter and a sprinkle of chopped chives if using. Serve immediately while hot and creamy.