The Best Way To Clean A Messy Panini Press Is Also The Simplest - Tasting Table
Briefly

Cleaning a panini press can be easy with the right tools; a damp paper towel, sponge, and warm soapy water can clear debris without scratching.
Avoid using sharp objects like steel wool and knives for cleaning, as they can scratch the panini press's non-stick surface and lead to food contamination.
Read at Tasting Table
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