When someone mimics your accent, they’re performing their limits, not yours.

An imitation like that is a small show about the person doing it. They are demonstrating that a different sound strikes them as remarkable, which says something about where they have been and who they have listened to. You are only the material they borrowed; nothing about you is being revealed.

You do not owe them a reaction, and the quietest response is usually the most expensive one for them. Keep talking in your own voice and let the moment sit there unlaughed at. If the same person keeps doing it, say once that you want it to stop, then stop explaining.