Step 1

Arrange a rack in the top third of the oven and heat the oven to 400°F. Coat an 8x8-inch or other 2-quart baking dish with butter or cooking spray.

Step 2

Peel and chop 3 pounds Yukon gold potatoes into 1-inch pieces. Place in a large pot and add enough water to cover the potatoes by 2 inches. Bring to a boil over high heat. Reduce the heat to maintain a simmer and cook until the potatoes are tender and can be easily poked with a paring knife, 7 to 10 minutes. Meanwhile, make the milk mixture and grate the cheese.

Step 3

Place 3/4 cup whole milk, 4 tablespoons unsalted butter, 1 teaspoon kosher salt, and 1/4 teaspoon black pepper in a medium saucepan over medium heat. Gently warm, whisking constantly, until the butter is melted, about 3 minutes. Remove from the heat and whisk in 1 cup sour cream.

Step 4

Shred 8 ounces sharp cheddar cheese (about 2 cups). Finely grate 1 ounce Parmesan cheese (about 1/2 packed cup).

Step 5

When the potatoes are ready, drain through a heatproof colander and place the colander over the pot. When the potatoes are cool enough to handle but still warm, return to the pot, and mash with a potato masher until mostly smooth (a few lumps are fine). (Alternatively, pass the potatoes through a ricer or food mill back into the pot.)

Step 6

Pour the milk mixture over the potatoes and stir to combine. Add the shredded cheddar cheese and stir to just combine (the cheese won’t be completely melted). Taste and season with more kosher salt and black pepper as needed.

Step 7

Transfer the mashed potatoes to the prepared baking dish and spread into an even layer. Sprinkle with the Parmesan. Bake until warmed through, about 20 minutes. Switch the oven to broil and broil until the top in golden-brown, 2 to 3 minutes more. Garnish with finely chopped chives or parsley, if desired, and serve.