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Material - Make outside plane invisible?

I have a plane mesh actor going through another static mesh actor. My goal is to use this plane as a texture to make it look like there is something in a bowl mesh. Is it possible to make a material that will turn the outside area of the plane invisible using the bowl mesh’s geometry? Using a radius to determine the visible area is not an option since not all my meshes are spherical.

If this is possible can someone point me in the right direction or give an example?