Cut the pressed tofu into bite-sized cubes. In a large skillet or wok, heat 1 tablespoon of vegetable oil over medium-high heat. Add the tofu cubes and cook until golden brown on all sides, about 8-10 minutes. Remove the tofu from the skillet and set aside.

In the same skillet, add the remaining tablespoon of vegetable oil. Add the sliced mushrooms, bell pepper, and broccoli florets. Stir-fry for about 5-7 minutes until the vegetables are tender-crisp.

Add the minced garlic and ginger to the skillet, stirring for an additional 1-2 minutes until fragrant.

Return the cooked tofu to the skillet. Pour in the soy sauce and sesame oil, stirring to combine.

Add the cornstarch mixture to the skillet and cook for another 2-3 minutes until the sauce thickens.

Remove from heat and garnish with sliced green onions and sesame seeds before serving.