The lead data protection supervisory authority will be that of the principal establishment, i.e. the place of the central administration in the EU.
If you do not have a central administration in the EU, then it will be the establishment in the EU where the essential part of your processing activities take place. For example, a commercial office.
The one-stop shop mechanism enables organisations that carry out cross-border processing (establishments in several EU Member States or processing operations affecting persons in several EU Member States) to communicate with a single national supervisory authority, which will take decisions applicable to all Member States concerned by the processing operations.