Slice your block of tofu into rectangles that are approx. ¼ inch thick.
Then place a clean dish towel (or paper towels) on a cutting board and arrange the slices in a single layer on top. Add another clean towel on top of the slices, followed by another cutting board (or flat baking pan). Then finally, place something heavy like a cast iron pan, or heavy books on top. Keep it like this for 15 minutes.
Meanwhile, add all the marinade ingredients to a small bowl and stir to combine.
Arrange the pressed tofu in a wide but shallow dish in a single layer and pour the marinade on top. Refrigerate for 60 minutes, and carefully flip the slices at the halfway point.
When your tofu has about 10 minutes of soak time left, preheat the oven to 400°F/204°C and line a baking sheet with parchment paper. Arrange the slices in a single layer and bake for 15 minutes. Then flip them and bake another 15-18 minutes.NOTE: Reserve the marinating liquid!
Optional: For grilling the smoked tofu
Heat a nonstick grill, or lightly grease your grill if needed.
Pour the leftover marinade into a small saucepot and add ⅓ cup of water and a tablespoon of tapioca flour. Whisk well and simmer over medium heat for 2-3 minutes to thicken and make your BBQ sauce.
Brush both sides of the smoked tofu slices with your sauce and place them on the grill on a diagonal to make grill lines, approx. 1-2 minutes on each side.
Notes
Plan ahead! You can marinate the tofu one day in advance to save time on the day you're serving it.
Although the total time required is a little over 2 hours, note that this is not all active time and the tofu marinates in the fridge for 1 hour.
Leftovers will keep in the fridge for 3-4 days in a sealed container.