Combine soy sauce and next 3 ingredients (through cornstarch).
Cut pork crosswise into 1/4-inch-thick slices. Stack several slices vertically; slice pork into 1/4-inch-thick pieces. Repeat procedure with remaining pork.
Add pork, carrots, and mushrooms to soy sauce mixture; toss.
Heat a large skillet over medium-high heat.
Add 1 tablespoon oil.
Add 1/4 cup onions; saut 30 seconds.
Add shredded cabbage and water; saut 2 minutes.
Remove cabbage mixture from pan.
Add remaining 1 tablespoon oil.
Add remaining 1/2 cup onions and garlic; saut 30 seconds.
Add pork mixture; saut 3 minutes or until done.
Add cabbage mixture; toss.
Place about 1/3 cup pork mixture into each of 8 reserved cabbage leaves.