Prepare the Chicken: Slice each chicken breast in half lengthwise to create four thinner cutlets. Season both sides with salt and freshly ground black pepper.
Sear the Chicken: In a large skillet over medium-high heat, warm the coconut oil. Add the chicken cutlets and cook for 3-4 minutes per side, or until golden brown and nearly cooked through. Remove the chicken from the skillet and set aside.
Sauté Aromatics: In the same skillet, add the minced garlic and grated ginger. Sauté for about 1 minute, or until fragrant.
Prepare the Sauce: Pour in the coconut milk and chicken broth, stirring to combine. Add the lime juice, lime zest, soy sauce, and brown sugar. Bring the mixture to a gentle simmer.
Combine and Cook: Return the seared chicken to the skillet, nestling it into the sauce. Reduce the heat to low, cover, and let it simmer for 5-7 minutes, or until the chicken is fully cooked and the sauce has slightly thickened.
Serve: Garnish the chicken with chopped fresh cilantro and serve with lime wedges on the side. This dish pairs wonderfully with steamed rice or sautéed vegetables.