In a 12-inch skillet, place kasha; cook and stir over medium-high heat until fragrant, about 2 minutes; remove to a bowl.
Heat oil in the same skillet; add eggplant, onion and garlic; cook and stir until onion is tender, about 3 minutes. Add chicken broth; bring to a boil; stir in toasted kasha.
Cover and reduce heat to medium-low; cook until liquid is absorbed, about 9 minutes. Let stand 3 minutes. Stir in tomato and olives. Transfer to a bowl and sprinkle with basil. Serve with grilled lamb chops, if desired.