Wrap a paper towel (or clean dish towel) around the block of tofu. Place the wrapped tofu on a plate, and press the tofu with a heavy pot or another comparable object—the weight of the pan alone will do. After 30 minutes, remove the pot and towel, then cut the tofu into medium-small cubes. Pat the cubes dry, with a fresh towel if necessary.
Heat oven to 425. In a medium-large bowl, gently toss the tofu in 1 teaspoon oil to evenly coat. Add the sesame and toss to coat. Then add the tapioca flour and toss until the tofu is coated in a thin layer of the sesame and flour.
Spread the tofu out on a parchment lined metal baking pan, then bake for 15 minutes. Flip, then bake another 10 minutes, or until the tofu is crispy and light golden brown.
Meanwhile, whisk the warm water, tahini, lemon juice, maple syrup, cayenne, black pepper, and salt together until combined. Taste, and adjust accordingly.
After flipping the tofu, heat 1/2 teaspoon oil in a medium-small nonstick skillet over medium heat. Add the broccoli, then cover and cook, stirring and flipping occasionally. If using fresh broccoli, you may need to add a splash of water to the skillet to steam-cook. Season with 1 teaspoon lemon juice, black pepper and salt.
Scoop the cooked tofu and broccoli into a bowl, then top with the grated carrot, tahini sauce, a drizzle of balsamic, seeds and gomasio.