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Set a 12-inch heavy-bottomed skillet over a medium-high flame. Season the chicken with sea salt and pepper. Add the olive oil to the pan, followed by the chicken breasts. Cook until golden brown and firm, about 8 minutes per side. Remove to a plate to rest for 10 minutes.
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Meanwhile, toss the romaine, cabbage, carrots and scallions in a large salad bowl.
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In a small food processor, pulse the peanuts until coarsely chopped. Transfer to a small bowl and set aside.
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Add the peanut butter, honey, tamari, juice of half a lime, and cayenne to the processor and puree until smooth, adding up to ¼ cup water to get the dressing thin enough to drizzle. (Alternatively, you can chop the peanuts and whisk the dressing by hand).
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Slice the chicken into thin strips and arrange on top of the romaine. Drizzle with the dressing and gently toss to coat.
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To serve, divide the salad between 4 plates and sprinkle with the chopped peanuts, and garnish with the remaining half a lime, but into quarters.