Step 1

Separate the cloves in 1 head of garlic and peel the cloves. Place in a small saucepan and add 3/4 cup olive oil. Bring to a simmer over medium heat. Reduce the heat to maintain a low simmer and cook, stirring occasionally, until the garlic is knife tender, about 30 minutes.

Step 2

Using a slotted spoon, transfer the garlic to a cutting board and use the flat part of a chefs’ knife to mash into a paste. Keep the oil in the saucepan.

Step 3

Peel and cut 3 pounds Yukon Gold potatoes into 1-inch pieces. Place in a large saucepan or pot and add enough cold water to cover by about 1 inch. Add 1 tablespoon of the kosher salt and bring to a boil over medium-high heat. Reduce the heat to maintain a simmer and cook until the potatoes are knife-tender, 12 to 15 minutes.

Step 4

Meanwhile, cut 8 tablespoons unsalted butter into 8 pieces and refrigerate until ready to use. Transfer all but 2 tablespoons of the garlic oil to a bowl or airtight container and reserve for another use. Add the mashed garlic, 3/4 cup whole milk, and 1/3 cup heavy cream to the saucepan. Bring to a simmer and cook until the mixture is just warmed through but not boiling, about 5 minutes.

Step 5

When the potatoes are ready, drain and return to the pot. Add the butter and remaining 2 teaspoons kosher salt. Mash with a potato masher until the butter is melted. Add the garlic mixture 1/4 cup at a time, mashing until fully absorbed into the potatoes. Taste and season with freshly ground black pepper and more kosher salt as needed.