Preheat the oven to 400°F (205°C). Line a large sheet pan with parchment paper.
Shred the pressed tofu using the large holes of a box grater or crumble it finely with your hands. Transfer to a bowl and add 1½ tbsp olive oil, cornstarch, ginger powder, garlic powder, paprika, black pepper, and soy sauce. Toss gently until evenly coated.
1 block tofu, 2 tbsp olive oil, 2 tsp cornstarch, 1 tsp ginger powder, 1 tsp garlic powder, 1 tsp paprika, 1 tsp black pepper, 1 tbsp soy sauce
Spread the shredded tofu out in an even layer on the prepared sheet pan. Bake for 25–30 minutes, stirring once halfway through, until golden, dry, and lightly crispy around the edges. Set aside.
While the tofu bakes, whisk together all simple sauce ingredients in a small bowl and set aside.
Heat the remaining ½ tbsp olive oil in a large skillet over medium heat. Add the fresh garlic and grated ginger and cook for about 30 seconds, just until fragrant.
2 cloves garlic, 1 tbsp ginger
Add the cabbage mix and shredded carrot. Stir-fry for 4–6 minutes, until softened but still slightly crunchy.
3 cups cabbage mix, 1 medium carrot
Add the baked shredded tofu to the skillet and toss to combine. Pour in the sauce and cook for 1–2 minutes, stirring, until everything is evenly coated and glossy.
½ tbsp soy sauce, 1 tsp sesame oil, 1 tbsp rice vinegar
Remove from heat and fold in the green onions, cilantro, and sesame seeds. Serve warm.
2 green onions, 2 tbsp cilantro, 1 tbsp sesame seeds