Preheat oven to 170°C fan-forced. Heat half the duck fat in a large deep casserole over medium-high heat. Brown rabbit in batches, turning occasionally, until golden (6-8 minutes). Remove rabbit from pan and transfer to a bowl. Deglaze with wine, scraping base of the pan until reduced by half (1-2 minutes). Pour wine mixture over rabbit. Wipe casserole clean with paper towel. Heat remaining duck fat in casserole over medium heat. Add onion, capsicum, celery and fennel; cook, stirring occasionally, until softened (8-10 minutes). Add tomatoes, stock and olive brine; stir to combine. Return rabbit and wine juices to casserole. Bring to a simmer. Cover with a tight-fitting lid and braise in oven until meat is very tender but still attached to the bone (2-2½ hours).

Meanwhile, for potato purée, place potatoes in a saucepan and cover with cold salted water; bring to the boil, then cook until potatoes are tender (15-18 minutes). Drain; cover with a tea towel and stand to steam (5 minutes). Pass through a ricer or mouli into a clean pan. Warm cream, butter, nutmeg and pepper in a saucepan, then gradually add to puréed potato, beating well between each addition, until smooth. Season. Keep warm.

Remove rabbit from braising stock. Return casserole to medium-high heat, and simmer until sauce is thickened (5-6 minutes). Stir through olives; return rabbit to sauce and turn to coat. Season with pepper.

Arrange rabbit in a serving dish and scatter with basil. Serve with potato purée drizzled with extra butter and scattered with chives on the side.