Combine hot water and shiitake mushrooms in a bowl; let them stand for 20 minutes. Drain mushrooms in a colander and save the liquid in another bowl. Rinse mushrooms. Remove and discard stems. Set aside.
Heat a wok over high heat. Add 1 tablespoon of oil and ginger to it; cook 30 seconds. Add reserved mushrooms; stir fry 1 minute.
Stir oyster sauce, sugar and cornflour in a small bowl; add into mushrooms. Add reserved mushroom liquid and stock; bring to a boil. Cover, reduce heat to medium-low, and simmer 20 minutes or until the sauce is thickened. Remove from heat; keep warm.
Heat the wok over high heat. Add remaining tablespoon oil to pan. Add garlic; stir-fry 10 seconds. Add broccoli; stir-fry 2 minutes or until cooked. Add mushroom and salt; cook 2 minutes, then serve.