Drizzle 1 tablespoon olive oil over the eggplant halves in a microwave-safe bowl and sprinkle with salt. Cover with a microwave-safe plate and cook on high for 5 minutes.
Meanwhile, toast the pine nuts in a skillet over high heat, about 1 minute; transfer to a bowl and add the remaining 3 tablespoons olive oil to the skillet. Season the chicken cutlets with salt and pepper and dredge in the flour, shaking off the excess. Add to the skillet and cook until brown on one side, 2 to 3 minutes. Flip the chicken, add the garlic and cook 2 more minutes. Remove the eggplant from the microwave, cool slightly and slice into chunks. Reduce the skillet heat to medium-low; add the sun-dried tomatoes, eggplant, basil, nuts and chicken broth to the skillet and bring to a simmer.
Transfer the chicken to plates; top each with ricotta and the eggplant mixture. Serve with the bread.