Mix together the ingredients for the tofu marinate: 3tbs tamari or soy sauce and cayenne pepper.
Press the tofu: See my post on Crispy Baked Tofu for step-by-step pictures on how to press tofu. Depending on the thickness of your tofu block, you may need to slice it into halves of thirds. The slices should be 3/4 inches thick. Wrap the slices in a kitchen towel and place a heavy pot on top for about 20 minutes. If you are in a rush, press the tofu between your hands with a kitchen towel to press out as much liquid as possible. Cook the white rice according to package instructions in salted water. I recommend cooking 3/4 cup for two people.
While the tofu is being pressed, preheat the oven to 400° F/ 205°C. Prepare the tofu marinade: In a shallow container that will allow all of the tofu cubes to lay flat, mix together the soy sauce and cayenne pepper. Once the tofu is finished being pressed, cut into small equal sized cubes and add to the marinade. Allow the tofu to sit in the marinade for about 5 minutes to absorb some of the soy sauce. Add the cornstarch one tablespoon at a time, mixing with the tofu to coat until all of the tofu is evenly coated.
On baking sheet that has been prepared with oil or lined with parchment paper (parchment paper sticks less), lay out the tofu evenly and bake in the oven for 10 minutes.
While the tofu is baking, mix together the sauce in a medium-sized bowl: soy sauce, apple cider vinegar, water, brown sugar or coconut sugar, and corn starch.
Remove the tofu from the oven and flip the cubes using a spatula in order to avoid the coating from sticking to the baking sheet. Move the tofu over to one side of the baking sheet and drizzle the other side with olive oil. Lay the broccoli pieces evenly on the other side and return to the oven for an additional 15 minutes, until the tofu is browned and crunchy on the edges. Remove from the oven.
Heat medium-sized frying pan over medium heat, add the sauce that you previously mixed together. Stir constantly as the sauce will start to thicken and you will need to keep it from sticking to the bottom of the pan. Stir until a thick sauce forms, about 2 minutes. Add the tofu and broccoli to the sauce and mix well.
Serve over white rice and sprinkle with sesame seeds.