Preheat your oven to 400°F (200°C) and line a large rimmed baking sheet with parchment paper.
Drain the extra firm tofu and press it between heavy plates or a tofu press for 15 minutes to remove excess moisture.
Cut the pressed tofu into 1-inch cubes and slice the carrots and parsnips into 1/2-inch thick rounds.
In a large mixing bowl, combine the tofu cubes, carrots, and parsnips with the olive oil, tossing until every piece is lightly coated.
In a separate small bowl, whisk together the nutritional yeast, garlic powder, onion powder, sea salt, black pepper, and smoked paprika.
Sprinkle the seasoning mixture over the tofu and vegetables, tossing again to ensure a thick, even coating on all sides.
Spread the mixture in a single layer on the prepared baking sheet, making sure the pieces are not touching to allow for maximum crispiness.
Roast for 25 to 30 minutes, flipping the tofu and vegetables halfway through, until the tofu is golden-brown and the root vegetables are tender.