Turn on oven to 400°. Line two baking sheets with parchment paper and place eggplant and tomatoes on backing sheet. Sprinkle 1 tsp salt and drizzle 3 tbsp olive oil over the eggplant and sprinkle ½ tsp salt and drizzle 2 tbsp olive oil over tomatoes,
Bake eggplant and tomatoes for 20-25 minutes or until soft but not charred. Toss around 15 minute mark. When done, remove from the oven and set aside.
While eggplant and tomatoes are roasting, cook pasta according to instructions on box. Drain the pasta. Transfer pasta to a large mixing bowl, add olive marinade and toss to combine.
Heat medium cast iron skillet over medium heat and place marinated chicken breast and rosemary sprigs. Sear each side of chicken breast until golden brown. Once chicken is thoroughly cooked, slice and set it aside. Chop browned rosemary leaves and combine with chicken slices.
In a large mixing bowl with pasta, add roasted eggplant, olives, chicken slices, and goat cheese. Toss ingredients together until well combined.
Transfer pasta salad to a large serving platter and add roasted tomatoes on top. Garnish with fresh basil leaves and serve slightly warm or chilled.