1. Combine vinegar, 1 tablespoon soy sauce, garlic, 1 teaspoon oil, Sriracha, and ginger in a bowl. Add tofu; toss gently to coat. Cover and chill 30 minutes.
2. Combine 2 cups boiling water and mushrooms in a bowl; cover and let stand 20 minutes. Drain mushrooms in a colander over a bowl, reserving liquid. Rinse and slice mushrooms; set aside. Strain reserved liquid through a paper towel–lined colander into a bowl; discard solids.
3. Heat a Dutch oven over medium-high heat. Coat pan with cooking spray. Add tofu mixture to pan; sauté 7 minutes or until liquid evaporates, stirring occasionally. Remove tofu from pan. Heat remaining 1/2 teaspoon oil in pan. Add remaining 1 tablespoon soy sauce, slaw, onions, and mushrooms to pan; sauté 2 minutes or until slaw wilts. Add reserved mushroom liquid, tofu mixture, and broth to pan; bring to a boil. Cover, reduce heat, and simmer 5 minutes. Place 3/4 cup noodles in each of 4 bowls. Pour 1 3/4 cups slaw mixture over each serving.