Preheat oven to 400 degrees. Spray a baking sheet lightly with nonstick spray.
Pierce potatoes all over with a fork, then place directly on the oven rack. Bake until tender (test with a fork), about 45 to 60 minutes.
While potatoes are baking, cook broccoli in microwave according to package directions (do not overcook). Let broccoli cool slightly, then cut any large chunks into bite-sized pieces. Season with salt and set aside.
Remove cooked potatoes from oven and set aside to cool. Reduce oven heat to 375 degrees.
When potatoes are cool enough to handle, slice off the top third. Remove potato flesh from the top slice and add it to a large bowl. Discard skin. Using a small spoon, scoop flesh from potatoes and add to bowl, leaving a ¼-inch shell. Set potato skins on baking sheet.
Add sour cream, butter, Dijon, and garlic powder to the bowl with the potato, then mash potatoes until everything is well combined. Stir in ½ cup cheddar cheese and season to taste with salt.
Add broccoli to potatoes and mix well.
Stuff each potato skin with ¼ of the mashed potato mixture, then sprinkle with remaining cheese.
Bake potatoes until cheese is melted and potatoes are heated through, about 25-30 minutes.