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Sauté the aromatics. Heat the olive oil in a medium stockpot over medium heat. Add the carrot, shallot, jalapeno, or serrano pepper. Cook for 5-6 minutes, until softened and fragrant. Stir in the garlic and ginger. Cook for about 30 seconds.
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Pour in the chicken broth and the vinegar; bring to a simmer. Taste the broth; adjust seasoning to taste.
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Add the cabbage stems and cook for 2–3 minutes. Then add the leafy tops and cook 1-2 more minutes.
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Remove from heat, portion into two bowls, and finish with sesame oil. Garnish with add-ins of choice- all are delicious!