Planchar oreja (plan•CHAR oh•EH•kha) literally means 'to iron ear'. When one is asleep in bed, one's head is putting preasure on an ear against the pillow, just like an iron puts preasure on a shirt against an ironing board. Hence planchar oreja means to be asleep. This is a funny, informal expression and it is not offensive.
CEO: ¿Por qué no viniste a la reunión trimestral de la junta de gobierno?
CFO: Me quedé planchando oreja, es que acabamos el reporte a las 4 de la mañana.
CEO: Why you did not make it to the quarterly meeting of the board?
CFO: I overslept. We finished the report at 4 in the morning.