How to Make It
In a blender, puree the basil, garlic, ginger, shallot, jalapeño, lime zest and juice and wine until smooth. Add the miso and honey and puree until very smooth. With the machine on, add the olive oil.
In a large glass dish, generously season the chicken with salt and coat with the marinade. Let stand for at least 15 minutes or up to 8 hours.
Light a grill. Wipe the marinade off the chicken, season with salt and grill skin side down over moderately high heat until the chicken releases easily from the grill, about 8 minutes. Turn and grill until the chicken is white throughout, 10 to 12 minutes longer, then serve.