Preheat the oven to 350 degrees F.
Use a fork to poke holes in the potatoes and place on a baking sheet. Bake until cooked through, about 1 hour. Use a sharp knife to test for doneness; it should easily cut into the center.
Meanwhile, in a large skillet over medium heat, cook the bacon until crisp, 8 to 10 minutes. Drain on a towel-lined plate, then crumble and set aside.
Bring a large pot of lightly salted water to a boil; prepare an ice water bath. Cook the broccoli florets in the boiling water until crisp-tender, 2 to 3 minutes. Drain and transfer to the ice bath, then drain again.
To serve the potatoes, make a cut through the top of each and push both ends together to fluff the potatoes. Season with salt and pepper, then top each with 1 tablespoon butter, a dollop of sour cream, 1/4 cup broccoli, 1/4 cup Cheddar, 2 tablespoons crumbled bacon and 1 tablespoon chopped chives. Return to the oven until the cheese melts, about 10 minutes.