Prick the potatoes several times with a fork. Microwave on high until tender and a fork easily slides into the center, 12 to 15 minutes. Transfer the potatoes to a bowl and cover with a plate or foil to keep warm.
In a medium microwave-proof bowl, combine the broccoli, butter, ½ teaspoon salt, and ¼ teaspoon pepper. Microwave on high for 3 minutes, stir once, then microwave until hot, 3 to 4 minutes more.
Split the potatoes (be careful of the steam). Top with the broccoli mixture and sour cream and sprinkle with ¼ teaspoon pepper.
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