In a saucepan, combine the soy sauce, sugar, and vinegar. Cook over low heat until the marinade thickens, 5 to 7 minutes. Cut the tofu into four 1-inch-thick burgers; transfer to a bowl, pour the marinade over the top, and let sit 15 minutes, turning once. Place on a medium-hot grill and cook 1 to 2 minutes per side. (To cook on a stovetop, heat the olive oil in a grill pan over medium heat and cook the tofu 2 minutes per side.) Top each burger with some of the Cheddar and cook 2 minutes more or until the cheese melts. Top with some sprouts and sliced radishes. Serve on the whole-wheat rolls with mustard, if desired.