Between paper towels, pat tofu dry. Brush baking sheet with 1 tsp of the oil. Arrange tofu on pan; brush remaining oil over top. Broil, about 8 inches (20 cm) from heat, until crisp and dry looking, about 15 minutes.
Meanwhile, in steamer, cover and steam broccoli until tender-crisp, about 3 minutes.
To make the Peanut Sauce:
In a small bowl, whisk together peanut butter, ginger, soy sauce, vinegar, sesame oil and chili paste; slowly whisk in 1/4 cup of hot water. Stir in onions.
Serve tofu over broccoli. Drizzle with peanut sauce; sprinkle with sesame seeds.