Cut tofu in half widthwise. Keep the pieces stacked and cut lengthwise into thirds (creates 6 rectangles), and then cut the tofu horizontally (slicing parallel to work surface) into quarters to create 24 cubes, each about 1 inch. Repeat with second package of tofu for a total of 48 pieces. Place tofu in a serving bowl and nestle the bowl in a larger bowl filled with crushed ice. Cover and refrigerate for at least 30 minutes or up to 2 hours.
Meanwhile, place dipping sauce ingredients in a small bowl and whisk until well blended; set aside.
Prepare five or more condiments and place each in a separate bowl or dish. Serve tofu family style in its chilled bowl with condiments, dipping sauce, and individual serving dishes.