Place the tofu on a cutting board and slice lengthwise into 4 equal pieces. Cut those down the middle to make 8 squares. Line a baking sheet with 3 layers of paper towels and arrange the tofu squares on it. Top with 3 more layers of paper towels, then put the cutting board and something heavy on top. Let the tofu drain about 5 minutes.

Pour the sesame seeds into a shallow dish and dredge the tofu pieces in sesame seeds until both sides are coated. In a large non-stick pan or well-seasoned cast iron skillet, heat 1 tabplespoon of the sesame oil over medium heat. Cook the tofu 4-6 minutes on each side, until golden brown. Add the tamari or soy sauce and toss the tofu until the tamari is absorbed, about 1 minute. Transfer the tofu to a dish and wipe the skillet out with a paper towel. 

Pour 1/2 cup of water into the skillet, then add the broccoli, salt, and pepper. Cover and simmer for 5 minutes, until the broccoli is tender. 

Divide the tofu and broccoli among 4 plates, drizzle with the last tablespoon of sesame oil, and serve.