Return 0 in GROUP BY when COUNT(*) is NULL

Question

Here is my original query:

SELECT
    CAST(IndexedDate as varchar),
    COUNT(*) AS Logins
FROM
    Table
WHERE
    EventType = 'Login'
AND IndexedDate > DATEADD(mm, -1, GETDATE())
GROUP BY
    IndexedDate
ORDER BY
    IndexedDate DESC

This would leave gaps, for example:

2016-09-13    41
2016-09-12    31
2016-09-09    15
2016-09-08    36

Based on this question, I tried the following and still received the gaps but on top of that the results were wrong (the numbers were MUCH higher):

SELECT
    CAST(IndexedDate as varchar),
    SUM(Case When COUNT(*) Is Null Then 0 Else COUNT(*)  End) AS Logins
FROM
...

How can I get my results to look like this?

2016-09-13    41
2016-09-12    31
2016-09-11    0
2016-09-10    0
2016-09-09    15
2016-09-08    36

I've checked a few other questions but they all involve joins or other factors not in my scenario.

---

UPDATE

Based on comments, I've attempted an OUTER JOIN. This iteration finally ran successfully, but the results were a bit backwards...

SELECT
        CAST(a.IndexedDate as varchar) as dt,
        COUNT(*) AS Logins
FROM 
        (
        SELECT *
        FROM Table
        WHERE IndexedDate > DATEADD(mm, -1, GETDATE())
        AND EventType = 'Login'
        ) a
FULL OUTER JOIN (
        SELECT DISTINCT(IndexedDate)
        FROM Table
        WHERE IndexedDate > DATEADD(mm, -1, GETDATE())
        ) b
ON 
        a.IndexedDate = b.IndexedDate
GROUP BY
        b.IndexedDate
ORDER BY
        b.IndexedDate DESC

Results:

2016-09-13    41
2016-09-12    31
(null)    1
(null)    1
2016-09-09    15
2016-09-08    36

I verified that aggregate b includes the missing dates.

Answer 1

So I flipped the aggregates from the edit to my original post and now it's working:

Query

SELECT
        CAST(a.IndexedDate as varchar) as dt,
        COUNT(EventType) AS Logins
FROM 
        (
        SELECT DISTINCT(IndexedDate)
        FROM Table
        WHERE IndexedDate > DATEADD(mm, -1, GETDATE())
        ) a
FULL OUTER JOIN (
        SELECT *
        FROM Table
        WHERE IndexedDate > DATEADD(mm, -1, GETDATE())
        AND EventType = 'Login'
        ) b
ON 
        a.IndexedDate = b.IndexedDate
GROUP BY
        a.IndexedDate
ORDER BY
        a.IndexedDate DESC

Results

2016-09-13    41
2016-09-12    31
2016-09-11    0
2016-09-10    0
2016-09-09    15
2016-09-08    36

Note that I had to replace COUNT(*) with COUNT(EventType) so it wouldn't count the date from the aggregate which was resulting in a 1.