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.
It might exist in a a different form, where you can independently create, just not copy.
You can’t put egg on your challah and then claim that nobody else is allowed to unless they pay you a fee.
No, but recipes are more unique than that.
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.
It’s a little easier to imagine, if you factor in precise measurements, ratios, rising time, baking time, etc. You may be right, though, there may be an umdina that individual recipes will be shared. But haga atzmicha, do you think I can buy a Susie Fishbein book and then share every recipe with you?