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. When the potatoes are nearly cooked (about 5 minutes remaining), add broccoli florets to the Dutch oven. 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.