Japchae

In a medium bowl, stir together soy sauce, brown sugar, garlic, and 1/2 teaspoon salt until sugar dissolves; set aside.

Bring a large pot of water to a boil. Add noodles and cook according to package instructions. Drain. Run under cold water to stop cooking; drain again, shaking to remove excess water. Transfer to a bowl and toss with sesame oil. Using kitchen shears, cut noodles in a few places.

Heat a large heavy-bottomed skillet (preferably cast iron) over high until smoking, 4 to 5 minutes. Add oil and swirl to coat. Add mushrooms and scallion lengths; cook, stirring, until softened and charred in places, 2 to 3 minutes. Add carrots, season with salt, and cook, stirring, until softened, 3 minutes. Reduce heat to medium; add spinach, soy mixture, and noodles. Gently toss to combine. Cook until heated through and sauce coats noodles, 2 minutes more. Adjust seasoning as desired. Sprinkle with scallion tops and sesame seeds; serve.