1. Spread the sesame seeds on a plate. Trim off and discard any fat from the chicken. Place the chicken between pieces of plastic wrap and pound lightly all over so the pieces have an even thickness (½ to ¾ inch). Season them lightly all over with salt and pepper, then gently press the chicken into the sesame seeds so the chicken is coated evenly.
2. Peel, then grate the ginger root to yield about 2 teaspoons. Finely grate the lime zest to yield about 1 teaspoon, then squeeze the lime(s) to yield about 2 tablespoons of juice. Coarsely chop the cilantro to yield 3 tablespoons.
3. Heat the vegetable oil and sesame oil over medium heat in a nonstick skillet that’s large enough to hold the chicken in a single layer. Add the chicken and cook for about 5 minutes, adjusting the heat as needed so the sesame seeds don’t burn. Turn the chicken over and cook for about 4 minutes, until it is cooked through and lightly browned. Transfer to a platter (preferably warmed) and cover loosely to keep warm.
4. Use paper towels to wipe out the skillet, then return it to medium heat. Add the butter and swirl to coat as it melts.
5. Add the ginger; cook, swirling or stirring, for a few minutes so the butter turns a light brown. Stir in the lime juice and the soy sauce until well incorporated.
6. Pour the pan sauce over the chicken, then sprinkle with the cilantro and lime zest. Serve right away.
Go to full version of