This dream made me think abouta saying which states "That you can see the true soul of a person trough her eyes". Probably, she asking you to hold her false eye might mean that she is not honest, or she might be also sight impaired ( spiritualy) and might not be able to see you and the world as it truly is.
When she starts talking about a topic which seems important to her, you offer her some of it, but you have a little left.
¿What do you have little left, that seems to be important for this woman? ¿Who is she? ¿Is she related to food preparation?
If you are a woman it might also simbolize an aspect of yourself, that is sight impaired and the other you have little to offer her.

Hope I have helped!

Sounds like you have as random dreams as I do!!

What an intreging dream. I love the imagery, a woman hands you her glass eye to hold. No, not glass. You called it her false eye. So now with her false eye in protective custody she goes about her business of being chef. At first I wondered if she removed it so it didn't fall into one of the dishes she was creating. I mean she can't see out of it, so being out of her head, and in your hand, at least she knew where it was. What does it represent? I'd guess there was some negative attitude towards woman involved.
Then again I ain't no psycologist.