Whisk buttermilk with garlic, table salt, sugar, paprika and lots of freshly ground black pepper in a bowl. Place chicken parts in a gallon-sized freezer bag (or lidded container) and pour buttermilk brine over them, then swish it around so that all parts are covered. Refrigerate for at least 2 but preferably 24 and up to 48 hours.
When ready to roast, preheat oven to 425 degrees. Line a baking dish with foil (not absolutely necessary, but Nigella suggested it and I never minded having dish that cleaned up easily). Remove chicken from buttermilk brine and arrange in dish. Drizzle lightly with olive oil, then sprinkle with additional paprika and sea salt to taste. Roast for 30 minutes (for legs; approximately 35 to 40 for breasts), until brown and a bit scorched in spots. Serve immediately.
Potatoes for a Crowd
In large bowl, combine all ingredients. Transfer to greased 11-in. x 13-in. baking dish. Bake, uncovered, at 350° for 45-55 minutes or until potatoes are tender.