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, 1/2 teaspoon salt, and 1/4 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 1/4 teaspoon pepper.