Preheat oven to 350 degrees F. Line a large baking sheet in foil or parchment and put it on the bottom rack of your oven to catch any drips from the potatoes.
Pierce the potatoes with a fork in a couple spots. Coat in olive oil and then in as much kosher salt as you can get to stick. Put them directly on the top rack and bake for about 90 minutes, depending on the size of your potatoes.
After potatoes are baked, remove from the oven and turn the heat to 400 degrees. Toss the broccoli with the olive oil and a pinch of salt and pepper. Lay it on a pan (it could be the foil lined pan from the bottom of the oven.) Roast the broccoli for 10-15 minutes, until tender and slightly charred.
Make the breadcrumbs by putting the bread and garlic in a blender or food processor (I used my Vitamix) and pulsing until you have crumbs. Transfer to a small bowl and add the olive oil. Set aside.
Put the butter, sour cream, and half the cheese in a large bowl. Cut the tops off the potatoes and scoop as much as you can out of the potatoes without breaking the skin. Add it to the bowl and mix. Season with salt and pepper (be careful with the salt however, as you’ll get residual salt from the potato skins.)
When the broccoli is done, toss it into the potato mixture and mix. Taste and season with salt and pepper.
Transfer the empty potato skins to the pan used for the broccoli and scoop the potato mixture inside, dividing it between the skins. Top the potatoes with the remaining cheese and the breadcrumbs and pop back in the oven. Bake until the cheese is melted and the top is brown. Let cool for a few minutes before serving.