For the kaffir lime pesto: Pulse the basil, cilantro, mint, oil, peanuts, garlic and lime leaves in a food processor until incorporated into a pesto and season with salt and pepper. Set aside while you cook the chicken.
Heat a cast-iron grill pan over medium-high heat and preheat the oven to 350 degrees F.
Brush half of the coconut milk on the skin of the chicken and place skin-side down onto the grill pan until crisp, 2 minutes. Brush the rest of the coconut milk on the other side of the chicken, and grill for another 2 minutes. Transfer the pan to the oven and bake until cooked through completely, 8 to 10 minutes. Remove the chicken from the pan and immediately toss in the pesto, allowing the heat to cook the pesto and release its fragrance and layers of avors. Squeeze the limes onto the chicken, plate and serve.
This recipe was provided by professional chefs and has been scaled down from a bulk recipe provided by a restaurant. The Food Network Kitchens chefs have not tested this recipe, in the proportions indicated, and therefore, we cannot make any representation as to the results.