Heat 1 tablespoon oil in a large nonstick skillet or wok over medium-high heat until very hot. Add tofu, and cook 6 minutes or until browned. Remove from skillet; set aside.
Combine soy sauce and next 3 ingredients; stir well, and set aside. Combine 1/4 cup water and cornstarch; stir well, and set aside.
Add 1 teaspoon oil to skillet, and place over medium-high heat until hot. Add 4 garlic cloves, and sauté 30 seconds. Add soy sauce mixture and remaining 1 cup water; cook 2 minutes. Add cornstarch mixture; bring to a boil, and cook 1 minute, stirring constantly. Return tofu to skillet, and cook for 1 minute or until thoroughly heated, stirring gently. Discard gingerroot. Spoon tofu mixture into a bowl; set aside, and keep warm. Wipe skillet dry with a paper towel.
Steam broccoli, covered, for 3 minutes or until crisp-tender. Remove from heat; set aside.
Heat remaining 2 teaspoons oil in skillet over medium-high heat. Add salt and 4 garlic cloves; sauté 1 minute. Add broccoli, and sauté 2 minutes. To serve, spoon tofu mixture over the broccoli.