For consistency with the corresponding feature in the glob function since Python 3.5, I would suggest to add an extra optional argument 'recursive' instead of 'glob_asterisks'. With the default recursive=False, one gets the old behavior, with recursive=True, it can handle the '**' and '*' as in pywildcard.

I realize that with recursive=False, the behavior is not exactly consistent with glob, but  I'd still prefer the same name for the optional argument. It is the common terminology for this type of feature. See https://en.wikipedia.org/wiki/Matching_wildcards