Refrigerate for at least 2 but preferably 24 and up to 48 hours.
Preheat oven to 425 degrees.
Drizzle lightly with olive oil, then sprinkle with additional paprika and sea salt to taste.
Line a baking dish with foil (not absolutely necessary, but Nigella suggested it and I never minded having a dish that cleaned up easily).
Remove chicken from buttermilk brine and arrange in dish.
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.
Roast for 30 minutes (for legs; approximately 35 to 40 for breasts), until brown and a bit scorched in spots.