Let's say I have a table with the following columns:

Employees Table

employeeID int
employeeName varchar(50)
managerID int
totalOrganization int

managerID is referential to employeeID. totalOrganization is currently 0 for all records.

I'd like to update totalOrganization on each row to the total number of employees under them.

So with the following records:

employeeID     employeeName     managerID     totalOrganization
1              John Cruz        NULL          0
2              Mark Russell     1             0
3              Alice Johnson    1             0
4              Juan Valdez      3             0

The query should update the totalOrganizations to:

employeeID     employeeName     managerID     totalOrganization
1              John Cruz        NULL          3
2              Mark Russell     1             0
3              Alice Johnson    1             1
4              Juan Valdez      3             0

I know I can get somewhat of an org. chart using the following CTE:

WITH OrgChart (employeeID, employeeName,managerID,level)
AS (
    SELECT employeeID,employeeName,0 as managerID,0 AS Level
    FROM Employees
    WHERE managerID IS NULL
    UNION ALL
    SELECT Employees.employeeID,Employees.employeeName,Employees.managerID,Level + 1
    FROM Employees INNER JOIN
    OrgChart ON Employees.managerID = OrgChart.employeeID
   )
SELECT employeeID,employeeName,managerID, level
FROM OrgChart;

Is there any way to update the Employees table using a stored procedure rather than building some routine outside of SQL to parse through the data?