I'll have a double
A slow day, even for a Monday, so let’s liven it up with double possession.* You can even call it the double genitive if you like to imagine that English is like Latin.
In the double possessive, you indicate possession with both the possessive form of a noun or pronoun and the preposition of. You talk about a friend of mine; if you said a friend of me, it would (or should) strike you as odd.
Don’t worry about the logic of this; it is an idiomatic construction, and Merriam-Webster’s Dictionary of English Usage says that it goes back “before Chaucer’s time.”
It also serves in some cases to eliminate an ambiguity, as Merriam-Webster’s explains: If you were to write Jane’s picture, you could be understood to mean a picture of Jane or a picture belonging to Jane. The double possessive makes clear that you mean the latter.
This construction is not a problem for native speakers, who grasp the idiom. If someone misguidedly made you sensitive to it, you can safely cross it off the list of things to worry about.
*Or, if you missed it over the weekend, you could have a look at the “Maxims for editors” post.