It was a regular event in the past years for our UK CAA inspectors going to the US to inspect and issue EASA approvals. Its been my understanding that the EASA stopped that process stating that an individual member state could not give an approval to a 'third country'. They subsequently inspected and approved ATOs themselves. I don't know whether EASA created a department or a staff role to do this or subcontracted out as and when required.
The UK is already a third country: so how then can, let us say, France or a German NAA travel to the UK, inspect and give an EASA approval? It is my understanding that a ATO will need to apply to EASA directly for an approval as we are witnessing from the EASA list.