Let's first see if we can agree that this addition is useful.

What's the purpose of this function?
Why would I use this function instead of yesodSpecWithSiteGenerator?

The use-case is as follows:

I have a Yesod site that contains the information necessary to call an external web service: Url and port, for example.
I am also the author of the external web service and would like to test how these two interact.
I would like to use testWithApplicationSettings to start the web service around the test.
That means I need something like SpecWith Wai.Application.
The port automatically gets chosen when this application is started, so the Yesod site needs to be made with the IO Site function only after this port is available.
This is why I need an argument to the IO Site function. (It is the yesod equilavent of beforeWith)

I hope the above clears up the need and the purpose of this new function.
I am very open to changing the specifics as long as my use-case can be supported.

We definitely need a Haddock for this. (Also, when written, we need a @SInCE comment, ChangeLog entry, and cabal file version bump.)

Will do that if you agree that this is a useful change.

I wasn't objecting to the inclusion of the function, something which takes an argument like this seems fine. But it needs a more descriptive name and Haddocks.

Also, while we're at it: can't yesodSpecWithSiteGenerator be rewritten to use the new function, and avoid some code duplication?

@snoyberg Ready for more review.

Thanks!