Preheat grill for medium heat and lightly oil the grate.
Brush eggplant slices with about 1 tablespoon olive oil.
Grill eggplant on the preheated grill until tender and lightly browned, about 5 minutes per side.
Heat remaining 1 tablespoon olive oil in a pot over medium heat; cook and stir onion and garlic in the hot oil until onion is softened, 5 to 10 minutes. Add chicken broth, wheat berries, barley, cinnamon, nutmeg, salt, pepper, and allspice to onion mixture; bring to a boil. Reduce heat, cover pot, and simmer until wheat berries are tender and some liquid is still remaining, about 40 minutes.
Preheat oven to 350 degrees F (175 degrees C).
Stir tomatoes and black beans into wheat berries mixture; remove pot from heat. Stir eggplant into wheat berries mixture; pour into a 9x9-inch casserole dish. Sprinkle mozzarella cheese over mixture.
Bake in the preheated oven until cheese is melted, about 15 minutes.