In Persona Q Theodore is given the weapon maker as he will make the team armor and weapons. Through power spots scattered through the dungeons the team can gather materials for Theodore to make weapons for them. The video below will give you the basic idea. The thing is though it still doesn’t explain the apron.
Article:http://www.siliconera.com/2014/06/03/theodore-cooks-weapons-persona-q-shadow-labyrinth/
As always thank you for reading.