Press the Tofu: Wrap the tofu block in a couple layers of paper towels and weigh it down with a heavy object to press out the extra liquid for 20 to 30 minutes.
Prepare the Marinade: In a small bowl, mix together the soy sauce, mirin, rice vinegar, 2 teaspoons of vegetable oil, garlic, and ginger. Set aside.
Marinate the Tofu: Slice the pressed tofu into half-inch slices. Lay them in a single layer in a container and pour the marinade over them. Swirl the container to coat all pieces evenly and let rest for an hour.
Bake the Tofu: Preheat the oven to 375 degrees Fahrenheit. Place the tofu slices on a baking sheet lined with parchment paper. Bake for 15 minutes, flip the slices, and bake for another 15 minutes.
Rest the Tofu: Cool down the tofu and place it in an airtight container. Let it rest in the fridge for at least four hours, preferably overnight.
Prepare the Basting Sauce: Mix the smoked shoyu (or regular soy sauce with liquid smoke), maple syrup, and 2 teaspoons of neutral vegetable oil.
Broil the Tofu: Lay the tofu slices on a wire broiling rack. Baste with the sauce and broil in the oven until edges get slightly charred, about 3-5 minutes. Flip, baste again, and broil for another 3-5 minutes.