Preheat oven to 400º. Scrub potatoes and pierce a few times with a knife. Place in oven, directly on rack, and bake until easily pierecable with knife and skin is lightly crisp, about 50-60 minutes.
While potatoes bake, toss broccoli with olive oil, garlic, salt and pepper. Arrange on baking sheet or in roasting pan and place into oven with potatoes. Roast until tender crisp, about 15 minutes.
Whisk sauce ingredients together in a small bowl. Thin with water or additional milk if desired. Taste test and adjust seasonings to your liking.
Cut open potatoes and stuff with broccoli. Drizzle with tahini sauce and serve.
Recipe Notes
This recipe makes a very generous batch of tahini cheeses sauce. If you have some leftover, store it in sealed container and refrigerate. If it dries out a bit in the fridge, add a few splashes of water and whisk until smooth.