I have a hard time determining which recipes are which in her book because of the way she names them. I decided that the first recipe was Asiago because when I looked up Asiago in the index it leads me to that page, and that the second was parmesan because the index leads you to that page.
I agree with you, that the first recipe seems like the right one for parmesan. I compared all of the recipes from all of my books for parmesan and I see the basic parameters for the cheese, other than the washed part.
I think I'll just forget about that recipe for awhile and use the first one for the comparison notes.
Caldwell also does not let the culture ripen for very long before she adds the rennett. She explains this theory at the beginning of the chapter, how you need to get started without the PH level dropping very far. All of the other recipes ripen for 30 to 40 minutes, but she only ripens for 5 minutes.
I might make parmesan on Sunday, if it works out well. I will watch for your notes on your make to appear as well. I love knowing what other people did and how it turned out.