Add shim strips on the face of the stud wall that add up to 3cm. A bit less is usually better, and then you makup any deficit with mud (joint compound). Since this is a lot of material, you might just place the shims at regular untervals, such that you can screw through them to attach your plasterboard.

I like to glue and pneumatically nail such strips with 18 ga or thinner brads..

On another tack.. What about splitting the stud wall in two, make each 5cm thick, attach the top-bottom and sides to the original frame and leave a 3cm air gap between.

Add shim strips on the face of the stud wall that add up to 3cm. A bit less is usually better, and then you makeup any deficit with mud (joint compound). Since this is a lot of material, you might just place the shims at regular intervals, such that you can screw through them to attach your plasterboard.

I like to glue and pneumatically nail such strips with 18 ga or thinner brads..

On another tack.. What about splitting the stud wall in two, make each 5cm thick, attach the top-bottom and sides to the original frame and leave a 3cm air gap between.