In a 4- to 5-quart Dutch oven, cook potatoes, covered, in enough lightly salted boiling water to cover for 20 to 25 minutes or until tender; drain. Return the hot, drained potatoes to the hot Dutch oven. Add the 1/4 cup butter. Let stand, uncovered, for 2 to 3 minutes. Meanwhile, in a small saucepan, heat the milk over low heat until hot but not boiling.
Mash potatoes with a potato masher or beat with an electric mixer on low speed just until light and fluffy. Stir in the warm milk, Asiago cheese, pesto, salt and pepper. (If you like, substitute basil pesto for the sun-dried tomato pesto.) Gradually stir in additional milk to make potatoes desired creaminess. If desired, serve with additional butter.