1 pound root vegetables, such as turnips, parsnips, rutabagas, celery root, carrots, and/or sweet potatoes;
2 pounds starchy potatoes (such as russets);
1 to 2 tablespoons butter, at room temperature;
1⁄2 to 1 cup half-and-half or whole milk, warmed;
2 teaspoons kosher salt, plus more to taste;
1⁄4 teaspoon ground black pepper.
Peel the root vegetables and potatoes and cut them into 1-inch pieces. It’s important that all of the pieces be the same size so that they will cook at the same rate. Place them in a large saucepan and cover with cold water. Add 1⁄2 teaspoon kosher salt per cup of water. Bring to a boil over medium-high heat, reduce the heat, and simmer gently only until the vegetables are tender when pierced with the tip of a knife, about 30 minutes. Do not let the vegetables cook until they begin to fall apart or they will be too waterlogged to mash. Drain the vegetables in a colander, then return them to the still-warm pan to steam dry, about 2 minutes. The chunks of potato should look chalky along the edges.
Gently mash the vegetables with a handheld potato masher or the back of a large spoon. Leave them fairly coarse.
Gently stir in the butter and warm half-and-half. Season with the salt and pepper and serve soon.
Make-ahead note: This dish is best served as soon as it is made, but you can keep it warm for up to 2 hours by transferring the mixture into a large glass or metal bowl. Cover the bowl with plastic wrap or foil and set the bowl over (not in) a pan of gently simmering water. If the mixture gets dry, stir in more warmed half-and-half or stock. If you must, you can make the mash up to 1 day ahead. Spoon into a buttered casserole dish and dot the top with butter. Store covered and refrigerated. Reheat in a 350°F oven for about 20 minutes or in the microwave.