Bring 4 quarts water to boil in Dutch oven over high heat.
Whisk soy sauce, oyster sauce, hoisin sauce, sesame oil, and five-spice powder together in medium bowl. Place 3 Tablespoons soy sauce mixture in large zipper-lock bag; add beef and liquid smoke, Press out as much air as possible and seal bag, making sure that all pieces are coated with marinade. Refrigerate at least 15 minutes or up to 1 hour. Whisk broth and cornstarch into remaining soy sauce mixture in medium bowl. In separate small bowl, mix garlic and ginger with 1/2 teaspoon vegetable oil; set aside.
Heat 1 teaspoon vegetable oil in12-inch cast-iron or nonstick skillet over high heat until just smoking. Add half of beef in single layer, breaking up clumps with wooden spoon. Cook, without stirring, 1 minute. Continue to cook, stirring occasionally, until browned, 2 to 3 minutes. Add 2 tablespoons wine to skillet; cook, stirring constantly, until liquid is reduced and beef is well coated, 30 to 60 seconds. Transfer beef to medium bowl and repeat with remaining beef, 1 teaspoon oil, and remaining 2 tablespoons wine. Wipe skillet clean with paper towels.
Return skillet to high heat, add 1 teaspoon vegetable oil, and heat until just smoking. Add mushrooms and cook, stirring occasionally, until light golden brown, 4 to 6 minutes. Add scallions and continue to cook, stirring occasionally, until scallions are wilted, 2 to 3 minutes longer; transfer vegetables to bowl with beef.
Add remaining teaspoon vegetable oil and cabbage to now-empty skillet; cook, stirring occasionally, until spotty brown, 3 to 5 minutes. Clear center of skillet; add garlic-ginger mixture and cook, mashing mixture with spoon, until fragrant, about 30 seconds. Stir garlic mixture into cabbage; return beef-vegetable mixture and chicken broth-soy mixture to skillet; simmer until thickened and ingredients are well incorporated, 1 to 2 minutes. Remove skillet from heat.
While cabbage is cooking, stir noodles into boiling water. Cook, stirring occasionally, until noodles are tender, 3 to 4 minutes.
Drain noodles and transfer back to Dutch oven; add cooked stir-fry mixture and garlic-chili sauce, tossing noodles constantly, until sauce coats noodles. Serve immediately.
