Press the tofu for 20–30 minutes to remove excess moisture. Cut into cubes and coat with cornstarch, salt, and black pepper.
Heat vegetable oil in a large skillet over medium-high heat. Add the tofu in a single layer and cook until golden and crispy on all sides.
While the tofu cooks, whisk together the soy sauce, brown sugar, garlic, ginger, rice vinegar, sesame oil, cornstarch, and water. Simmer until the sauce thickens.
Add the crispy tofu to the sauce and gently toss until evenly coated.
Divide the cooked rice between serving bowls. Arrange the carrots, cucumber, edamame, and radishes around the rice.
Spoon the teriyaki tofu over the bowls, drizzle with any remaining sauce, and finish with sesame seeds and sliced green onions. Serve immediately.