Puree all sauce ingredients in a blender until smooth. Toast pitas on rack of a gas burner over high heat, turning with tongs, until heated through but still pliable (pitas may puff), about 1 minute, then wrap in foil to keep warm. (Alternatively, wrap untoasted pitas in foil and warm in a preheated 300°F oven or toaster oven.) Heat 1 tablespoon oil in a 12-inch heavy skillet over moderately high heat until hot but not smoking, then saute half of onions, stirring occasionally, until browned but still crisp, 4 to 5 minutes. Transfer to a large plate. Saute remaining onions in 1 tablespoon oil in same manner and transfer to plate (reserve skillet). Stir together coriander, cumin, salt, and pepper in a bowl. Pat beef dry and toss with spices. Heat 1 tablespoon oil in skillet over moderately high heat, then saute half of beef, stirring, until browned but still pink inside, 1 to 1 1/2 minutes. Transfer beef to plate with onions, then saute remaining beef in remaining tablespoon oil in same manner. Halve pitas and fill with beef and onions. Serve sauce on the side.