Heat one tbsp olive oil in heavy small saucepan over medium heat. Add garlic and chili; sauté until fragrant and lightly golden, about 3 minutes.
Add soy sauce, brown sugar, vinegar, and 3 tbsp water and bring to a boil, stirring until sugar dissolves.
Reduce heat to medium and simmer until reduced to 3/4 cup.
Remove bbq sauce from heat, and whisk in sesame oil. Transfer 1/4 cup bbq sauce to small bowl and reserve for serving.
Prepare bbq (or grill) to medium heat. Combine bok choy and eggplant in a large bowl. Drizzle with 2 tbsp olive oil and toss to coat. Sprinkle with salt and pepper.
Drizzle remaining oil over fish and sprinkle with salt and pepper.
Grill veggies and fish, turning occasionally and basting with the sauce until veggies are tender and slightly charred, and fish is just opaque in center (about 10 minutes for veggies, and 7 for fish).
Transfer all to plates and sprinkle with green onions and drizzle with remaining bbq sauce.