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Cooks' note:.
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Some sliced chicken breasts may not be of an even thickness. If necessary, put each paillard between 2 sheets of plastic wrap and pound with flat side of a meat pounder until about 1/4 inch thick.
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Special equipment:
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A well-seasoned large (2-burner) ridged grill.
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Prepare grill pan and start sauce:.
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Heat grill pan over moderate heat until hot.
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Meanwhile, simmer all sauce ingredients except butter in a 1-quart saucepan, uncovered, stirring occasionally, 2 minutes. Set aside while cooking chicken.
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Make paillards:.
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Cook cumin, paprika, and pepper in oil in a small skillet over moderately low heat, stirring, until fragrant, about 2 minutes. Transfer to a small bowl, reserving skillet for sauce (do not clean).
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Brush some spiced oil on 1 side of each paillard, then sprinkle with some salt. Arrange 2 paillards on grill, oiled sides down, and brush tops with some of spiced oil, then sprinkle with some salt.
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Grill 2 minutes, then turn over and grill until just cooked through, about 3 minutes more.
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Transfer to a platter and cover with foil. Grill remaining paillards in same manner, transferring to platter.
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Finish sauce:.
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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.
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Remove from heat, then add butter and swirl skillet until butter is just incorporated. Season sauce with salt and spoon over chicken.
