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Adjust rack to top position (top and middle positions for 4 servings) and preheat oven to 425 degrees. Wash and dry produce.
Dice potatoes into ½-inch pieces. Trim and thinly slice scallions, separating whites from greens; mince whites. Trim and halve Brussels sprouts lengthwise.
Place potatoes in a large 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; drain and return potatoes to pot.