Get charcoal started on grill. Or if you’re using a gas grill, do do that voodoo that you do so well.
Prepare chicken. Trim the tenderloins from the chicken breast halves [a chunk of meat often attached to the underside of the breast]. Place each breast half between 2 sheets of plastic wrap and pound with flat side of a meat mallet until about 1/4-inch thick or so. Or you can use the bottom of a heavy skillet as I did, not being able to find our mallet. And actually, I think the skillet worked better, flattening the entire paillard more evenly. I placed a cutting board under the meat to protect the countertop.
Make sauce. Simmer all sauce ingredients except butter in a 1-quart saucepan, uncovered, stirring occasionally, 2 minutes. Set aside while cooking chicken.
Make paillards. Cook cumin, paprika and pepper in oil in a small skillet over moderately low heat, stirring, until fragrant, about 2 minutes. Transfer spiced oil to a small bowl, reserving skillet for sauce [do not clean].
Brush some spiced oil on each side of paillards, then season with salt. When charcoal is ready, spread evenly in one layer and put grill in place. Oil it lightly and arrange paillards on grill. Grill 2 minutes, then turn over and grill until just cooked through, about 3 minutes more. Transfer to a platter and cover with foil.
Finish sauce. Pour sauce through a medium-mesh sieve into reserved small skillet, discarding solids. Add any juices from chicken accumulated on platter to sauce and bring to a boil. Add butter and swirl skillet until butter is just incorporated. Season sauce with salt and spoon over chicken. Serve.