Place rice noodles in a large heatproof bowl; pour boiling water over noodles. Let sit until translucent but still slightly chewy, 5 to 10 minutes. Drain, and set aside.
Heat a large saucepan over medium-high heat. Season beef with 1/2 teaspoon each salt and pepper, and rub with 1 tablespoon oil. Sear beef in pan until golden brown, 3 to 4 minutes. Sear other side, 3 to 4 minutes more. Remove beef.
Reduce heat to medium. Add remaining tablespoon oil, mushrooms, and garlic; cook, scraping up any browned bits, until mushrooms are tender, 3 to 5 minutes.
Add stock, soy sauce, vinegar, and 2 cups water to the pan; bring to a boil over medium-high heat. Remove from heat; stir in carrots, cabbage, scallions, and bean sprouts.
Cut beef diagonally into very thin slices. Ladle the broth and vegetables into serving bowls, and place the noodles and sliced beef on top.