Prepare the Potatoes: Cut the Yukon potatoes into 1-inch pieces, leaving the peels on or peeling them according to preference, then place them in a large pot.
Add Salted Water: Cover the potatoes completely with cold water and add 1 teaspoon of salt.
Boil Until Tender: Bring the pot to a boil, then cook the potatoes for 20 minutes, or until they are tender.
Drain the Potatoes: Drain the cooked potatoes thoroughly, then return them to the same pot while they are still warm.
Mash with Butter: Add the softened salted butter and mash the potatoes with a potato masher until they reach your desired consistency.
Add the Creamy Ingredients: Stir in the sour cream, half and half, and sharp cheddar cheese until the ingredients are evenly distributed.
Melt the Cheddar: Continue stirring until the cheddar has melted completely and is incorporated throughout the potatoes.
Finish with Chives: Fold in the chopped chives, then taste and season with additional salt as needed.
Serve Immediately: Transfer the finished mashed potatoes to a serving dish and serve immediately.