Set oven to 350ºF. Scrub and dry the potatoes and prick the skin with a fork in a couple places. Use a few drops of the oil on your ands to rub the potatoes down real good. Place on a small baking sheet. 

Toss the broccoli (or cauliflower) with the rest of the oil and put into a baking dish (preferably one with a lid) Sprinkle a bit of salt on the potatoes and the broccoli, then cover the broccoli dish. 

Bake potatoes and broccoli for about 30 minutes. Check the broccoli. It should be tender and roasted. Remove and let potatoes cook another 30 minutes until very tender. Let potatoes cool until you can handle them. (At this point you can also refrigerate the potatoes and broccoli for a few days.)

Halve potatoes and scoop out the insides leaving a shell about 1/4 inch thick. Combine the potato insides with the cottage cheese, roasted broccoli, salt, pepper and garlic. Mash until mostly smooth. 

Pile into shells and top each with 1/2 ounce cheddar (stop here and refrigerate or freeze if making ahead).

Return to the oven for 10 minutes until hot and melted.