Mistress Cogita says to check Snowpoint Temple to get one of the Plates.
Go to Snowpoint Temple
After you have talked to Mistress Cogita during The Researcher of Myths to begin this mission, go to the Alabaster Icelands and go north from the Pearl Settlement to reach Snowpoint Temple. Enter the temple and go to the guidance marker to find the sealed door. After Adaman and Sabi meet you, check on the door. Then make your way downward through the area. At the end, approach Adaman and Sabi.
Battle Regigigas
Approach Regigigas and the battle will begin. Reduce its HP and inflict status ailments to improve your chances of capturing it, then throw Ultra Balls (or whatever types of Poké Balls you have available) until you catch it.
Afterward, you get the Blank Plate.