Combine 2 tablespoons low-sodium soy sauce and cornstarch in a large bowl. Add cubed tofu and toss to make sure all the tofu is covered. Refrigerate for at least 15 minutes.

Heat vegetable oil in a wok or large nonstick skillet over medium-high heat. Add the tofu and brown on all sides. While that is working, combine the remaining 3 tablespoons of low-sodium soy sauce, 1 teaspoon cornstarch, vegetable broth, seasoned rice wine vinegar, minced green onions, ginger, garlic, and chile paste in a small bowl. Add to pan and cook, stirring constantly, for about 1 minute until thickened. Add broccoli; cover the pan and cook for just a few minutes, or until broccoli is tender. Add water chestnuts, green onion tops, and peanuts; stir to combine. Serve on top of hot rice.