Oil the grates of your grill to prevent the tofu from sticking. Preheat the grill to medium heat (375°F).
Place the tofu in a medium bowl. Toss wiith 1 tablespoon olive oil to coat. Set aside.
Make the pesto: In a food processor, add the basil leaves, pine nuts, and garlic. Pulse until the basil is coarsely chopped. Add the olive oil, vegan parmesan cheese, salt, and black pepper. Pulse until the mixture is well blended but still has a little bit of texture. Adjust seasoning to taste then pour over the tofu cubes and gently toss to coat.
Let the tofu marinate for at least 30 minutes, up to a few hours.
Thread the marinated tofu onto metal skewers. If you prefer wooden skewers, soak them in water for 30 minutes prior to use.
Place the tofu skewers onto the direct heat of the grill.
Cook for 5 minutes per side (the exact time may vary depending on your grill), basting the sides of the tofu with any extra pesto each time the skewers are turned. The tofu is done when there are visible grill marks and it is lightly golden brown. Serve warm or room temperature.