Press the tofu for 15 minutes to remove excess moisture, then cut into 1-inch cubes.
In a small bowl, whisk together peanut butter, minced garlic, grated ginger, soy sauce, sesame oil, and red pepper flakes until smooth. Add warm water if needed to thin the sauce.
Heat the cooking oil in a large wok or skillet over medium-high heat. Add the tofu cubes and cook until golden brown and crispy on all sides, about 8 to 10 minutes.
Remove the tofu from the pan. Add the broccoli florets and shredded cabbage to the wok, stir-frying for 4 to 5 minutes until tender-crisp.
Return the tofu to the wok. Pour the creamy peanut sauce over the mixture and toss well to coat evenly.
Cook for another 2 minutes until the sauce is heated through and slightly thickened.
Garnish with chopped green onions and sesame seeds before serving over warm rice.