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Adjust rack to top position and preheat oven to 425 degrees. Wash and dry produce.
Dice potatoes into ½-inch pieces. Trim green beans if necessary.
Place potatoes in a medium pot with enough salted water to cover by 2 inches. Bring to a boil and cook until tender, 15-20 minutes. Reserve ½ cup potato cooking liquid (¾ cup for 4 servings), then drain. Return potatoes to pot and cover to keep warm.
Cut broccoli into bite-size pieces if necessary. (Save green beans for another use.)