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Adjust rack to middle position (middle and top positions for 4 servings) and preheat oven to 425 degrees. Lightly oil a baking sheet. Wash and dry all produce.
Cut potatoes into ΒΌ-inch-thick rounds. (TIP: Cutting your potatoes into thin, uniform slices here is key! This will help them all roast at the same pace.) Cut broccoli florets into bite-size pieces if necessary.