You can cook this at a lower heat if you prefer–a sauté rather than a stir-fry. Just add a few minutes to each part of the cooking.
1/4 c vegetable or chicken broth
2 T mirin or sake; or 1/2 t sugar dissolved in 2 T white wine, vermouth or sherry
1 t arrowroot or cornstarch
1 t salt
2 T vegetable oil
1/2 t toasted (dark) sesame oil, or to taste
1 c carrots, coarsely grated or cut into julienne (matchsticks)
4 c thinly sliced Napa Cabbage
2 large garlic cloves, minced
2 t peeled, minced fresh ginger
2 scallions, thinly sliced, or 1/4 c chopped red onion
1. In a small bowl, stir together broth, mirin or sake, arrowroot, and salt until smooth. Set aside.
2. Heat a wok or a large, heavy-bottomed skillet over medium-high heat until hot. Add vegetable and sesame oils and heat until it just begins to smoke (if sautéing rather then stir-frying, you just want the oil to be hot). Add carrot and stir-fry 3 minutes. Add cabbage, garlic, and ginger and stir-fry another 2 minutes, or until carrots are crisp-tender. Whisk broth mixture once more and add to vegetables. Stir-fry an additional minute to coat. Add scallions or red onion and stir to combine. Serve immediately.