How to match ATC requirements to work in EU?
I would suggest to contact the IT ANSP and ask if they accept applications for ready entry ATCOS: https://www.enav.it/sites/public/en/LavoraConNoi/Traduzione-di-Contatti-n.html

In Germany we have plenty of so called „ready entries“ who applied for a job as ATC in Germany while holding a valid non-EU ATCO license.

After an assesment by our company and - hopefully - signing the contract they participate in some weeks of sim training to learn the procedures of the new sectors. After succesfully completing the sim phase the OJT (on the job training) begins. During something between 6 and 12 months they will train working in real world with a coach and finally take one examination per working position.
That‘s it!