In a medium bowl, whisk soy sauce, brown sugar, honey, vinegar, oil, ginger, and garlic until smooth. Pour marinade into a large resealable bag, carefully arrange tofu in bag, seal, and allow to marinate in refrigerator at least 2 hours or up to 4.
Remove tofu slabs from marinade and pat dry with paper towels (reserve marinade).
Grease the grates of a grill well with vegetable oil and preheat to 400F. Brush both sides of zucchini slabs lightly with oil and season with salt and pepper to taste.
Pour marinade in a small pan and bring to a simmer over medium-high heat. Reduce heat to medium-low and allow to simmer 4-6 minutes until sauce is reduced and thickened, stirring frequently. Keep sauce warm and set aside.
Arrange tofu and zucchini slabs in a single layer on preheated grill. Grill tofu and zucchini 3-4 minutes per side until lightly charred and grill marks appear.
Transfer tofu and zucchini to a serving tray and drizzle with sauce. Top with sliced green onions and sesame seeds and serve warm. Enjoy!