Heat stovetop or outdoor grill. Prepare rice according to package instructions.
Toss eggplant with vegetable oil and grill, turning occasionally to prevent burning, until eggplant is tender, about 20 minutes.
While the eggplant is cooking, in a medium bowl, whisk together the peanut butter, rice vinegar, lime juice, soy sauce , brown sugar, ginger and pepper flakes until smooth. Thin out the sauce with water to a medium thick, pourable consistency.
On a large platter, place rice on a bed of lettuce. Arrange eggplant over the rice. Drizzle with sauce. Garnish if desired.