Heat 1 teaspoon of the oil in a large skillet or wok over medium heat. Add the beaten eggs and scramble gently until just set, about 2 minutes. Transfer to a plate and set aside.
Add 1 tablespoon oil to the same skillet over medium-high heat. Add the onion and carrot and stir-fry for 3-4 minutes until starting to soften.
Add the cabbage, garlic, and ginger to the skillet and stir-fry for 5-6 minutes, tossing often, until the cabbage wilts and turns tender-crisp.
Pour in the tamari and rice vinegar, and toss to coat evenly. Return the scrambled eggs to the skillet and toss gently to combine, breaking the eggs into smaller pieces.
Season with salt and black pepper to taste. Divide among bowls, top with sliced scallions, and drizzle with chili crisp if using.
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