Place zucchini and squash in a strainer set over a bowl. Sprinkle with 1 Tbsp. salt and toss to combine. Let sit 10 minutes, then shake in strainer, pressing gently, to remove any excess liquid.
Meanwhile, whisk lemon juice, honey, pepper, 1/2 cup basil, 3 Tbsp. oil, and 1/4 tsp. salt in a large bowl.
Heat remaining 2 Tbsp. oil in a large skillet over medium. Cook garlic until it begins to sizzle and turn golden brown, 5–7 minutes. Using a slotted spoon, transfer to bowl with dressing. Increase heat to medium-high, add eggplant and 1 cup tomatoes, and cook, stirring occasionally, until eggplant is browned and cooked through and tomatoes begin to burst, about 6–8 minutes. Season with remaining 1/4 tsp. salt and transfer to bowl with dressing.
Cut remaining 1 cup tomatoes in half lengthwise and add to bowl with dressing. Add zucchini and squash; gently toss to combine. Add 3 Tbsp. olives and 2 Tbsp. basil, then transfer with tongs to a platter, letting extra liquid drain and remain in bowl. Lay mozzarella on 1 end of platter and drizzle with oil. Top dish with remaining 2 Tbsp. basil and 1 Tbsp. olives.
Serving Size 4 Servings
* Percent Daily Values are based on a 2,000 calorie diet. Your daily value may be higher or lower depending on your calorie needs.