Step 1

Place 1 tablespoon plus 2 teaspoons soy sauce, 1 1/2 teaspoons mirin, 1 1/2 teaspoons sesame oil, and 1 1/2 teaspoons packed dark brown sugar in a medium bowl and stir to combine.

Step 2

Trim the excess fat from 1 (8 to-10 ounce) boneless New York or ribeye steak. Cut in half horizontally (also known as butterflying), then very thinly slice across the grain. Add to the soy sauce mixture and toss to combine. Let sit at room temperature while you prepare the noodles and vegetables.

Step 3

Bring a large saucepan of heavily salted water to a boil over high heat. Meanwhile, prepare the vegetables.

Step 4

Prepare the following, placing each in a separate pile on a rimmed baking sheet or large plate: Peel 1 medium carrot and cut crosswise into thirds. Cut each piece lengthwise into 1/4-inch thick planks. Stack the planks and cut lengthwise into 1/4-inch wide matchsticks (about 1 cup). Thinly slice 1/2 medium yellow onion (about 1 cup). Trim the stems from 4 ounces fresh shiitake mushrooms and thinly slice the caps (about 2 cups). Finely chop 2 garlic cloves and pile on top of the mushrooms.

Step 5

Measure out 5 ounces baby spinach if needed (about 5 packed cups). Thinly slice 1 medium scallion if using.

Step 6

Add 8 ounces dried Korean sweet potato noodles to the boiling water and stir to separate them. Boil until cooked through, about 5 minutes. Meanwhile, place 3 tablespoons soy sauce, 2 tablespoons packed dark brown sugar, and 1/2 teaspoon of the kosher salt in a small bowl and stir until the sugar and salt are dissolved.

Step 7

Drain the noodles in a colander and rinse with cold water until cool. Leave in the colander and cut with kitchen shears into 6 to 8-inch lengths. Drizzle with 1 tablespoon of the sesame oil and toss to coat.

Step 8

If using beef, heat 1 tablespoon vegetable oil in a large frying pan (preferably nonstick) over medium heat until shimmering. Add the beef and spread into an even layer. Let cook undisturbed for 1 minute. Stir-fry until just cooked through, 30 seconds to 1 minute more. Using tongs, transfer to the colander with the noodles.

Step 9

Heat 1 tablespoon vegetable oil in the same pan (no need to clean) over medium heat until shimmering. (If not using beef, heat 1 tablespoon vegetable oil in a large frying pan.) Add the carrot, onion, remaining 1/2 teaspoon kosher salt, and 1/4 teaspoon black pepper. Cook, stirring occasionally, until the onion is softened and starting to brown, 6 to 8 minutes.

Step 10

Add the mushrooms and garlic and cook, stirring occasionally and scraping up the browned bits from the bottom of the pan with a wooden spoon, until the mushrooms are tender, 3 to 4 minutes.

Step 11

Add the spinach and cook until mostly wilted, about 2 minutes. Add the reserved noodles, beef, and soy sauce mixture. Toss until heated through and the noodles are evenly coated in sauce, 2 to 3 minutes.

Step 12

Remove the pan from the heat. Drizzle with the remaining 1 tablespoon sesame oil, sprinkle with 1 tablespoon toasted white sesame seeds, and toss to combine. Taste and season with more kosher salt and black pepper as needed. Garnish with the scallions and more sesame seeds. Serve warm or at room temperature.