Preheat the oven 450 F. Line 2 baking sheets with parchment paper.
Using the large holes of a box grater, grate the tofu (note: it’s helpful to press as much as water as possible out of the tofu before grating and baking). Add the tofu to a bowl and toss with 2 tablespoons of olive oil, plus the cornstarch and 1/2 teaspoon each of paprika, garlic powder, and onion powder. Add salt and pepper.
Spread the tofu in a single even layer on one of the baking sheets and set aside.
Add the rice to a bowl and toss with the remaining 2 tablespoons olive oil, plus 1/2 teaspoon each of paprika, garlic powder, and onion powder. Add salt and pepper.
Spread the rice in a single even layer on the second bake sheet. Add both baking sheets to the oven and bake for 35-40 minutes, until golden and crispy. Towards the end, you may want to keep an eye that it doesn’t start to burn - the edges will burn first. Remove from the oven and let cool.
Peel the carrots and grate them on the large holes of a box grater. Grate the cucumbers on the large holes of a box grater.
Add all of the dressing ingredients to a bowl and whisk well to combine.
Using your hands, gently break apart the crispy tofu and rice. In a large bowl, add the tofu, rice, carrots, and cucumber. Add the dressing and toss to combine. Garnish with green onion and sesame seeds.