Char-grill eggplants over a barbecue or under a grill until skin blackens. Cool, peel and cut into pieces. Peel and mince garlic.
In a heavy-based pan, heat oil, then add garlic, stirring until soft. Add beef mince and cook, stirring it with a spoon until beef loses its pinkness. Add eggplant, fish sauce and salt and pepper to taste. Turn down heat to simmer before covering. Cook and cover about 25 minutes or until eggplant has lost its firmness.