Place noodles in a large bowl; pour boiling water over noodles to cover. Let stand 6 minutes or until pliable, stirring occasionally to separate noodles. Drain. Combine stock, oyster sauce, soy sauce, sugar, and red pepper in a small bowl; whisk until sugar dissolves.
Heat a large nonstick skillet or wok over medium-high heat. Add beef to pan; cook 4 minutes or until beef is browned and crispy in places, stirring to crumble. Remove from pan.
Return pan to medium-high heat. Add oil; swirl to coat. Add garlic and ginger to pan; stir-fry 30 seconds. Add bok choy and mushrooms; stir-fry 2 minutes or until tender. Remove mushrooms and bok choy from pan. Add egg to pan; cook 30 seconds, stirring frequently. Return vegetables to pan.
Add noodles and beef to pan. Add stock mixture to pan; cook 1 minute or until bubbly. Remove from heat. Add basil and black pepper; toss to combine.