Preheat oven to 450° with rack in center.
Rub prepared potatoes with oil and salt.
Bake directly on the rack for 1 hour and 15 minutes, or until tender all the way through when pierced with a skewer.
Remove potatoes from the oven, split and cool slightly.
Scoop out and lightly mash the flesh (reserve skins); set aside.
Sauté onion in melted butter until soft, about 5 minutes.
Whisk in flour; cook 2 to 3 minutes.
Stir in broth and milk. Cook and stir until thick, 4 to 5 minutes.
Add potato and simmer 5 minutes. Mash the potato more for a creamier consistency.
Stir in parsley and salt & pepper.
Toss strips of potato skins in oil, salt, and pepper. Roast in 400° oven 15 minutes, or until crisp.
Serve soup warm and top with potato skins and sunflower seeds.