Combine first 5 ingredients (through pepper) in a bowl.
Combine 1/2 cup boiling water and mushrooms in a bowl. Let stand 15 minutes; drain, reserving the soaking liquid. Discard stems; thinly slice caps.
Heat oil in a large nonstick skillet over medium-high heat. Add ginger and garlic; sauté 30 seconds. Add lamb mixture; sauté 4 minutes. Stir in broth; bring to a boil. Cover and reduce heat; simmer 40 minutes. Uncover and bring to a boil; add carrot, mushrooms, and reserved liquid. Cook 5 minutes, or until slightly thick. Add oyster sauce and cilantro; serve with rice noodles.