How to Make It
In a small saucepan, combine the water, sugar and honey and cook over moderate heat, stirring until the sugar has dissolved, about 1 minute. Pour the mixture into a heatproof bowl and add the crushed red pepper. Let cool to room temperature. Add the vinegar and fish sauce and season with salt and black pepper.
Using the side of a chef's knife or a rolling pin, bruise the pieces of lemongrass. Transfer to a large, shallow dish. Add the cilantro, shallots and vegetable oil and mix well. Add the chicken and coat thoroughly with the marinade. Cover and refrigerate overnight. Bring the chicken to room temperature before grilling.
Light a grill or preheat a grill pan. Scrape the marinade off of the chicken breasts. Season the chicken with salt and pepper and grill, skin side down, over moderately high heat until the skin is lightly charred and crisp, about 3 minutes. Move the chicken to a cooler part of the grill or reduce the heat to moderate and grill for 2 minutes longer. Turn the chicken and cook until white throughout, about 5 minutes longer. Transfer the chicken to a cutting board and let rest for 5 minutes.
Slice the chicken crosswise 1/3 inch thick and transfer to plates. Sprinkle the chicken with the mint leaves and serve with lime wedges. Pass the dipping sauce at the table.