Does your EASA license have a SEL rating? You would then have two options. You could:
Complete a TSA background check.
Have your CAA verify your license to the FAA.
Walk into a FAA FSDO and walk out with 61.75 certificate based on your EASA license.
Or you could:
Complete a TSA background check.
Pass a FAA medical exam.
Log at least three hours training for SEL PVT.
Pass a PVT SEL checkride and have the PVT SEL rating added to you FAA ATP.
If your EASA license does not have a SEL rating the second option will be the only way.