Dissolve salt and sugar in 2 quarts cold water in large container. Immerse chicken and refrigerate until fully seasoned, about 1 hour. Meanwhile, adjust oven rack to lower-middle position and heat oven to 500°.
Line bottom of broiler pan with foil and spray with nonstick vegetable cooking spray. Remove chicken from brine and rinse thoroughly under cold running water. Following illustrations 1 through 6, butterfly chicken, flatten breastbone, apply flavored butter (if using), and position chicken on broiler pan rack; thoroughly pat dry with paper towels.
Toss potatoes with 1 tablespoon oil, salt and pepper to taste in medium bowl. Spread potatoes in even layer in foil-lined broiler pan bottom. Place broiler pan rack with chicken on top. Rub chicken with remaining 1 1/2 teaspoons oil and sprinkle with pepper.
Roast chicken until spotty brown, about 20 minutes. Rotate pan and continue to roast until skin has crisped and turned a deep brown and an instant-read internal thermometer registers 160° in thickest part of breast, 20 to 25 minutes longer. Transfer chicken to cutting board. With potholders, remove broiler pan rack; soak up excess grease from potatoes with several sheets paper towels. Remove foil liner with potatoes from broiler pan bottom and invert foil and potatoes onto cookie sheet or second cutting board. Carefully peel back foil, using a metal spatula to help scrape potatoes off foil as needed. With additional paper towels, pat off remaining grease.