Preheat the oven to 425°F. Line a baking sheet with parchment paper.
Use a tofu press to remove excess water from the block of tofu. Pat the tofu dry with paper towels.
In a large bowl, whisk together the olive oil, chili powder, garlic powder, salt, black pepper, and smoked paprika.
Tear the pressed tofu into bite-size pieces. Add the tofu to the bowl with the spice mixture and toss gently to coat.
Arrange the tofu in a single layer on the parchment-lined baking sheet. Bake for 35 minutes, turning halfway through. Remove from the oven, but keep the oven on.
Transfer the cooked tofu to the large bowl. Add 1/4 cup barbecue sauce and toss gently to coat.
Return the barbecue sauce-coated tofu to the baking sheet and bake for an additional 15 minutes.
Toast the burger buns, then spread each with 1 tablespoon of barbecue sauce.
Pile on the BBQ tofu and serve warm.