Pesto Smashed Potatoes

Make-Ahead: The pesto can be prepared up to 1 day ahead, covered and refrigerated. Bring to room temperature before using. The potatoes can be prepared up to 4 hours ahead, stored in a cool place. Cook the potatoes just before serving.

Pesto
1 cup packed fresh basil leaves
1 cup freshly grated Parmesan cheese
1/2 cup extra-virgin olive oil
3 garlic cloves, chopped
4 pounds red- or yellow-skinned potatoes, scrubbed, but unpeeled
4 tablespoons unsalted butter, at room temperature
Approximately 1/2 cup milk, heated
1/2 teaspoon salt
1/4 teaspoon freshly milled black pepper

To make the pesto, place the basil, cheese, and garlic in a food processor fitted with the metal blade. With the machine running, add the oil through the feed tube and process until smooth. (The pesto can also be made in a blender, in two batches.) Transfer to a bowl and cover with plastic wrap. (The pesto can be prepared up to 1 day ahead, covered and refrigerated. Bring to room temperature before using.)

Fill a large pot (at least 5 quarts) halfway with cold water. Peel the potatoes and cut into chunks about 1 1/2 inch square, and drop them into the pot. Add more cold water to cover the potatoes by 1 to 2 inches. (The potatoes can be prepared up to this point for 4 hours, stored at cool room temperature.)

Stir in enough salt to the pot until the water tastes mildly salted. Cover tightly and bring to a full boil over high heat. Depending on your stove and the size of the pot, allow about 20 minutes for the water to come to a boil.

Reduce the heat to medium-low and set the lid askew. Cook at a moderate boil until the potatoes are tender when pierced with the tip of a small, sharp knife, 15 to 20 minutes. Do not overcook the potatoes.

Drain the potatoes well and return to the still-warm cooking pot. Add the pesto and butter. Using an electric hand mixer, mash the potatoes, gradually adding enough milk to reach your desired consistency. Season with the salt and pepper. Transfer to a warmed serving dish and serve immediately.