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Place the flours in a large bowl and mix together. Toss the chicken in the flour until it is lightly dusted.
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Put 2 tablespoons oil in a large skillet, preferably nonstick, and turn heat to medium-high. When the oil is hot but not smoking, add chicken in one layer. (If oil smokes, it will taste bad.)
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Sprinkle with salt and pepper and cook until the chicken is golden on one side, about 4 minutes. Toss the chicken until just about done: smaller pieces will take 5 minutes total, larger pieces about 10. Transfer to a plate. Remove pan from the heat and let it cool for a moment.
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Add the remaining oil to the pan and return it to medium high heat. Add the garlic, shallots and the cayenne pepper and cook, stirring, for about 2 minutes. Add the ketchup and the red wine vinegar and stir; cook until ketchup bubbles then darkens slightly, about 2 minutes, stirring regularly.
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Return chicken to the pan and stir to coat with the ketchup sauce.
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Transfer to a serving dish, squeeze lime juice over the chicken, adjust the seasoning, garnish with the basil leaves if you like, then serve.