We like to butcher our own chicken for these airline breasts, but this is something you can ask your butcher to do for you if you don’t have the chops. Butchering your own chicken means you get the breasts for this recipe then thighs and drumsticks for other meals, plus you can make stock with the chicken bones. Here’s how to cut these airline breasts: Start by using a sharp knife to split the skin between the breasts along the breast bones. Then cut through the skin between the breast and thigh on each side. Then use the knife to cut off just the tip (aka the flat) of each wing. Finally use that sharp knife slice the breast off the chicken by slicing between the breast and rib bones. At this point you can remove the leg quarts as well and save them for another recipe – like these Buffalo Leg Quarters.
Season the airline breasts on all sides with kosher salt and insert your Meater Probe, if using. Heat a grill or smoker to medium heat and add the breasts. Cook for 17 to 20 minutes or until the breast hit 165 degrees F. Remove from the grill and set aside to rest. While the chicken rests, grill the asparagus. Toss the asparagus with olive oil and season with salt and pepper. Grill the stalks directly on the grates until charred, about 6 minutes. Add the lemon and grill until just charred. Set the asparagus and lemon aside while you sear the chicken and make the pan sauce.
Heat a large skillet over medium high heat. Add the chicken breast, skin side down and cook until crisped and golden, about 4 minutes. Remove the chicken from the pan and immediately add the the garlic and 1 tablespoon of butter, the soy sauce, honey, lemon and lime juices. Cook until reduced, just a minute or so then remove from the heat and add the green onion, parsley, and remaining two tablespoons of butter and stir until the sauce is thickened.
Serve the sauce over the chicken breast and asparagus.