Slice tofu into ½-inch slices. Lay slices on a paper towel to remove excess moisture.
Whisk remaining tofu ingredients in a bowl.
Place tofu in a shallow dish, and cover with marinade. Cover and refrigerate 15 minutes, or up to 24 hours.
For dressing, place all ingredients in a sealable container and shake vigorously. Can be refrigerated up to 3 days.
Prepare grill. Thoroughly clean and oil. Preheat to medium high. If no grill, preheat broiler on medium heat with rack 6 inches from the top.
For salad, remove greens from carrots; chop greens into small, bite-sized pieces. Chop kale and cabbage into ¼-inch shreds. Place all greens in a large mixing bowl.
Peel carrots. Use a spiralizer to spiral-cut carrots and zucchini into long, noodle-like pieces. Add to mixing bowl with greens.
Cut top and bottom off watermelon radish. Using a mandolin slicer, a chef knife or a slicing blade on a food processor, slice radish paper-thin. Place in salad bowl with greens and vegetables.
Grill marinated tofu until grill marks appear, 1½ to 2 minutes per side. Remove from heat, and cut into thinner slices or square cubes. If no grill, place tofu in a 9×13-inch baking dish and broil, flipping once, until golden brown, approximately 4 minutes.
Toss all greens and vegetables with dressing; disperse among 6–8 salad bowls. Top with tofu; garnish with toasted sesame seeds.