Place 2 1/2 cups of the tamari and the raw sugar in the insert of a non-reactive double boiler. Reserve the remaining 1/2-cup of tamari. Fill the bottom of the boiler with 3-inches of water. Assemble the boiler and place over a medium-low flame. Cook the tamari mixture until it reduces to make a light syrup. This should take 60 to 90 minutes and yield 1/4 cup of tamari syrup.
Meanwhile, trim the tofu slices to make each a perfect rectangle. Pour 1/4 cup of the reserved tamari onto a plate. Place the tofu slices over the tamari, then pour the remaining 1/4-cup of tamari over the tofu. Be careful to pour the tamari so each slice is completely covered with tamari. Marinate 1 hour.
Place the tofu slices onto a cookie sheet or baking pan and baste with a thin coating of the tamari syrup. Place under a preheated broiler 4-inches from the heat and broil 2 to 4 minutes, or until the tofu jiggles like hot custard. Use the leftover tamari marinade to baste the tofu as it cooks so the tofu doesn't dry out. Toss the cucumber and pickled ginger in a small mixing bowl with the yuzu and mirin. Arrange 2 tofu slices per plate and place the cucumber salad against the tofu slices. Sauce the tofu with the miso sauce and any remaining tamari syrup.
Combine ingredients in the cup of an immersion blender and blend until smooth. Thin with water if desired.