Transact SQL :: Recursive CTE To Fetch Parent

I am using the following code to get the next immediate parent of a customer in the hierarchy and it works fine. However, it works only for one customer at a time (i made this a scalar function and I pass the customer id as shown below).

How can I modify this so that i can get each customer and its next immediate parent (all of them in one shot in a single data set)?

WITH my_cte (CustomerID, ParentID, Level)
AS
(
SELECT CustomerID, ParentID, 0 AS Level
FROM [dbo].MyTable
WHERE CustomerID = @CustomerID

UNION ALL
SELECT CustomerID, ParentID, Level + 1
FROM [dbo].MyTable e
INNER JOIN my_cte AS cte ON e.CustomerID = cte.ParentID
)

select CustomerID from my_cte WHERE Level <> 0 AND Level = (SELECT MIN(Level) FROM my_cte WHERE Level <> 0)