1. Prick potatoes in several places with a fork. Microwave on high until tender (a paring knife inserted in the center of each should meet no resistance), 13 to 15 minutes, turning once during cooking. Set aside.

2. Cut broccoli into small florets (reserve stems for another use). Place in a microwave-safe bowl filled with 1 inch of water. Season with coarse salt and ground pepper. Microwave on high until crisp-tender, 3 to 5 minutes. Drain.

3. Meanwhile, cut a deep cross in the top of each potato; push ends toward each other to open. With a fork, loosen and lightly mash inside. Dividing evenly, top potatoes with butter, cheddar cheese, and broccoli.