Cut block of tofu in half (so you have 2 square blocks) and then slice each block lengthwise into thirds to make square patties.
Drain the tofu.
If baking, preheat the oven to 450F. Combine the rest of the marinade ingredients in a shallow dish and marinate the tofu patties for 35 minutes, flipping halfway through.
Scrape off the extra marinade before cooking and reserve the excess.
Heat a small saucepan over medium-low and add the leftover marinade. Bring to a simmer and cook until just thick. Remove from heat.
Baking: Place patties on a baking sheet lined with parchment paper. Bake for 10 minutes, flip and bake for another 10 minutes. Top with 1/2 of the thickened glaze and bake for 4 minutes, flip and top with the remaining glaze and bake for another 4 minutes. Warm buns in the oven during the last 2-4 minutes of cooking time.
Pan-frying: Heat 1/2-1 tbsp oil over medium-high heat in a large skillet. Place patties in hot oil and cook until browned around the edges, about 5 minutes, flip and brown the other side. Top with 1/2 of the thickened glaze and flip, cooking until the glaze bubbles and thickens. Top with the remaining glaze, flip and cook until both sides are coated with glaze.