Preheat grill over medium heat. With knife, cut eggplant flesh in crosshatch fashion, brush with 2 tbsp. EVOO and season. Cover and grill until soft, 20 minutes. Scoop flesh into blender; puree with nutmeg. In saucepan, heat remaining EVOO over medium heat; add onion and rice and stir, 5 minutes. Add wine, then broth, 1/2 cup at time, and cook, stirring, until absorbed, 20 minutes. Stir in eggplant; season. Top with basil and more nutmeg.