Roast lamb in a 350°F (180°C) oven for 20 minutes. Spoon rice mixture into the centre, and return to oven until lamb reaches desired doneness, about 15 minutes for medium rare 160°F (70°C) (time will vary significantly, depending on the size of the lamb).
Let rest 10 minutes before serving.
While lamb is resting, in medium saucepan, melt butter over medium-high heat. Cook shallots, until tender, about 5 minutes. Stir in wine and cook until reduced by half, about 3 minutes. Add broth and chives and cook down until slightly thickened, about 2 minutes. Spoon sauce over servings of lamb alongside rice.