Place tofu between several layers of paper towels. Place a heavy plate on top of tofu, and let stand 20 minutes. Cut tofu crosswise into 4 pieces.
Combine mirin and next 8 ingredients (mirin through garlic) in a bowl, stirring with a whisk.
Heat a large nonstick skillet over medium-high heat. Add tofu pieces; pour mirin mixture over tofu. Bring to a boil; cook 4 minutes. Turn tofu pieces over; cook 3 minutes. Remove from heat, and keep warm.
Bring broth to a boil in a Dutch oven. Add bok choy; cover and cook 2 minutes or until crisp-tender. Drain.
Place 1 cup soba noodles on each of 4 plates; top each serving with 1 tofu piece. Spoon about 1 tablespoon sauce over each tofu piece; sprinkle each serving with 1 tablespoon green onions and 1/2 teaspoon toasted sesame seeds. Arrange 2 bok choy halves on each plate.