Using a tofu press; remove the excess fluid from the tofu. If you don't have a tofu press; slice tofu into 2–3 slabs and place between paper towels or clean kitchen towels. Place a cutting board and heavy objects on top and allow tofu to press for 15–30 minutes to remove excess moisture.
Preheat oven to 400°F and line a baking sheet with parchment paper.
Cut the tofu into cubes and transfer to a large bowl.
Drizzle with olive oil and toss gently. Sprinkle with cornstarch, garlic powder, smoked paprika, oregano, salt, and pepper. Toss until evenly coated.
Spread tofu evenly on the prepared baking sheet. Bake for 15 minutes, flip, and bake an additional 15 minutes until golden and crisp.
Prepare the dressing.
In a small bowl or measuring cup, whisk together olive oil, red wine vinegar, lemon juice, oregano, salt, and pepper.
Assemble the bowls.
Divide cucumbers, tomatoes, peppers, and red onion between bowls. Top with crispy tofu and feta if desired. Drizzle with dressing before serving.