For the sake a readability, I would break the problem into two parts.
First, figure out how many recordings each person has for a day. This is the query in the common table expression (the first select statement). Then select against the common table expression to limit the rows to only those that you need.
with cteRecordingsByDate as
(
SELECT Person.FirstName,
Person.LastName,
cast(created as date) as Whole_date,
Count(Recordings.ID) AS Recording_COUNT
FROM Recordings
JOIN Person ON Recordings.PersonID=Person.ID
WHERE Created BETWEEN '2013-08-01 00:00:00.000' AND '2013-08-21 00:00:00.000'
GROUP BY Person.FirstName, Person.LastName, cast(created as date)
)
select FirstName, LastName, count(*) as Days_Above_100
from cteRecordingsByDate
where Recording_COUNT > 100
order by count(*) desc