Plastering over the roller shutter box? Tips? How to best approach it?

Hello everyone,

we would like to plaster over the [Raffstore-kästen] on our extension so that the boxes are not visible in the end.

The box depth according to the manufacturer is 12 cm, with a plaster angle additionally mounted on it. So I estimate that the box then has a depth of just under 13.5 cm.

The box is mounted directly on a wooden beam (our extension is built using timber frame construction).

How thick does the insulation need to be that is installed next to the box so that I can plaster over the box? Is 12 mm insulation sufficient for this?

Sorry, maybe my question is totally stupid, but I really have no idea how much insulation I need to use on the extension to get the 13.5 cm box plastered over.

Many thanks in advance.

Best regards
Oli

Here is a sketch so that you can better understand what I mean. :)

I am concerned about the yellow-marked area:
How thick do I have to choose the insulation so that the box is plastered over in the end and no longer visible from the outside?