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.
Whisk lemon juice, honey, pepper, 1/2 cup basil, 3 Tbsp oil, and 1/4 tsp salt in large bowl.
- Heat remaining 2 Tbsp oil in a large skillet over medium heat. Cook the garlic until it begins to sizzle and turn brown (5-7 minutes). With a slotted spoon, transfer the garlic to the bowl with the dressing.
Increase heat to medium-high and add the eggplant and 1 cup of tomatoes and cook, stirring occasionally, until the eggplant is browned and cooked through and the tomatoes begin to burst (6-8 minutes). Season with the remaining 1/4 tsp salt and transfer to the bowl with the dressing
Cut remaining 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 one end of the platter and drizzle with oil. Top the dish with the remaining 2 Tbsp basil and 1 Tbsp olives.