Slice eggplant in half lengthwise, and pierce skin with a fork. Cut tops off bell peppers; discard tops, seeds, and membranes. Place eggplant and bell peppers on a microwave-safe plate. Microwave on high for 8 minutes or until tender.
While the eggplant cooks, combine 1/4 teaspoon salt, ginger, garlic powder, and 1/8 teaspoon red pepper; sprinkle the chicken with the ginger mixture. Heat 1 teaspoon olive oil in a large nonstick skillet over medium-high heat. Add chicken, and cook for 6 minutes on each side or until chicken is done.
Combine eggplant and bell peppers in a blender or food processor. Add 1/2 teaspoon salt, 1/8 teaspoon red pepper, 1 teaspoon oil, paprika, and juice; process until smooth. Serve chicken with sauce.