Well, I only know how to talk about this by reference to american law, so I will.
1. This would be patent, since it is a method of doing something. I doubt halacha has a parallel to patent, since patent cannot exist without a centralized registry, since it gives rights to the person who invented even where another independently invents.
2. Even if there is patent in halacha, I doubt it would apply to a published recipe, since there is no reason to assume the author invented it, and anyway any variations are probably “obvious.” You can’t put egg on your challah and then claim that nobody else is allowed to unless they pay you a fee.
3. Even if this was patented, the author gave permission for others to use it by publishing the directions in a book. It is hard to imagine you can publish directions of how to do your patent in a book and then claim only those who buy the book may put egg on their challah.