How to Make It
Place steak in a small bowl. Add 1 1/2 tablespoons soy sauce, 1 1/2 teaspoons brown sugar, 1 1/2 teaspoons sesame oil, and 1 teaspoon minced garlic. Massage seasonings into meat. Let stand at room temperature until ready to cook.
Bring a Dutch oven full of water to a boil. Place a strainer basket in water. Add spinach to strainer; cook until just wilted, 30 seconds to 1 minute. Remove spinach from pot; drain. Rinse with cold water until cool. Press or squeeze spinach to remove excess liquid. Place spinach in a small bowl. Add 1 teaspoon sesame oil, 1/4 teaspoon salt, and remaining 1 teaspoon minced garlic; stir thoroughly to combine.
Return water to a boil. Add noodles; cook until al dente, 6 to 7 minutes. Drain noodles, and rinse with cold water. Drain well, and snip noodles a few times with kitchen shears. Place noodles in a large bowl. Add remaining 3 tablespoons soy sauce, remaining 2 tablespoons brown sugar, 2 tablespoons plus 1 teaspoon sesame oil, and 1/2 teaspoon salt; toss well to combine.
Heat Dutch oven over medium-high. Add 1 tablespoon canola oil; swirl to coat. Add carrots and scallion bottoms; cook, stirring often, 2 minutes. Add scallion tops and 1/4 teaspoon salt; cook, stirring constantly, 1 minute. Remove from pan.
Add 1 tablespoon canola oil to Dutch oven over medium-high; swirl to coat. Add mushrooms; cook until browned and tender, about 3 minutes. Add remaining 1 teaspoon sesame oil and remaining 1/4 teaspoon salt, tossing to coat. Remove from pan.
Add remaining 1 tablespoon canola oil to Dutch oven over medium-high heat; swirl to coat. Add steak mixture; cook until liquid evaporates and steak is browned and glazed, about 4 minutes. Add noodle mixture, spinach mixture, carrot mixture, and mushroom mixture; cook, tossing constantly, until heated through, about 3 minutes. Serve warm or at room temperature.