Pierce potatoes all over with a fork. Place in the microwave and cook at 50% power, turning once or twice, until the potatoes are soft, about 20 minutes. (Or, use the "potato setting" on your microwave and cook according to the manufacturer's instructions.)
Meanwhile, brown meat in a large skillet over medium-high heat, stirring often, about 3 minutes. Transfer to a large bowl. Increase heat to high, add broccoli and water to the skillet, cover, and cook until tender, 4 to 5 minutes. Drain the broccoli; add to the meat.
Carefully cut off the top third of the cooked potatoes; reserve the tops for another use. Scoop the insides out into a medium bowl. Place the potato shells in a small baking dish. Add 1/2 cup Cheddar, sour cream, salt and pepper to the potato insides and mash with a fork or potato masher. Add scallions and the potato mixture to the broccoli and meat; stir to combine.
Evenly divide the potato mixture among the potato shells and top with the remaining 1/2 cup cheese. Microwave on high until the filling is hot and the cheese is melted, 2 to 4 minutes.
Vegetarian variation: Replace the ground beef with a soy-based substitute or omit the beef altogether and increase the broccoli to 1 1/2 cups and the cheese to 1 1/4 cups.