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PLACE eggplants on lightly oiled baking sheet. Broil 3 to 4 inches from heat about 10 minutes or until skin chars and blisters, turning frequently. Cool eggplant slightly. Peel eggplant and cut diagonally into 1/4-inch thick slices.
MIX fish sauce, brown sugar, lime juice and chili sauce in small bowl until well blended. Set aside.
HEAT oil in wok or large skillet on medium-high heat. Add shallots and garlic; stir fry until golden brown. Add eggplant and sauce mixture; cook 2 minutes, stirring frequently. Gently stir in tofu and basil. Remove from heat. Cover. Let stand 5 minutes to blend flavors.