Place bulgur in a heatproof dish. Pour the boiling water over it and cover until water is absorbed, about 30 minutes. Fluff with a fork.
Heat the oil in a large skillet or wok. Add onion and sauté until translucent. Add garlic and continue to sauté until onion is lightly browned. Add mushrooms and cook until they've started expressing liquid and wilted. Stir in the bulgur and all remaining ingredients. Cook over low heat, stirring frequently for 10 minutes.