1 leek (white and pale green parts only), coarsely chopped
2 lb potatoes, preferably Yukon Gold or russet (baking) potatoes
4 carrots, cut into 1/2-inch chunks
2- to 3-inch cube of ginger
1/2 stick (1/4 cup) unsalted butter
3/4 cup whole milk
3/4 teaspoon salt
1/4 teaspoon black pepper
Wash chopped leek well in a bowl of cold water, then lift out and drain well.
Peel potatoes and cut into 2-inch pieces. Cover with cold water in a saucepan. Bring to a boil, then reduce heat and simmer, uncovered, until potatoes are tender, about 18 minutes.
Drain and return to saucepan. (see note below)
While potatoes are simmering, cook carrots in a 1- to 1 1/2-quart saucepan of boiling salted water until just tender, 5 to 6 minutes, then drain. (see note below)
Trim hard knobs, rough ends and dirty bits off ginger. Coarsely chop it by hand with knife then mince it in a food processor. Add carrots and process again until fairly smooth.
Cook leek in butter in a 10-inch skillet over moderately low heat, stirring occasionally, until very tender, about 6 minutes. Add milk, salt, and pepper and simmer, stirring, 2 minutes.
Add leek mixture to potatoes and coarsely mash with a potato masher, then stir in the carrot puree.
Note: Other veggies can be pre-cooked and added to the mash (rutabaga, turnips, cabbage, etc.). Other herbs and spices can be added (cumin, fresh thyme, etc).