You're not going to be able to get it directly from D21, D22, or D23.   The
only way I can think of is to extract the formula from those cells and then
get the date out of that.   Is there some reason you don't have the dates
stored elsewhere and then reference them for D21, D22 and D23?   That would
be far easier.

What would make your life a whole lot easiar is in the cell where you want
June 1, 2005... is to put June 1, 2005 in that cell. And then in the other
cell put.

="PAYE "&YEAR("CellWithDate")

If I understand you correctly, you wish to have a formula which will extract
the date you have entered in the DATE function argument.  So in the examples
you give, you will extract:

January 1, 2004
June 1, 2005
October 15, 2005

That being the case, you will need to use a VBA Function  (User Defined
Function or UDF).

To enter this function, <alt-F11> opens the VB Editor.

Ensure your project is highlighted in the Project Explorer window
Insert/Module and paste the code below into the window that opens.

To use the formula, enter it in some cell as

=GetDt(cell_ref)
or, in your case,

=GetDt(D21)

Format that cell as mmm dd, yyyy

================================================
Function GetDt(rg As Range) As Date
Dim oRegex As Object
Dim oMatchCollection As Object
Dim Y As Integer, M As Integer, D As Integer

Set oRegex = CreateObject("VBScript.RegExp")
oRegex.Pattern = "(\(DATE\()(\d{4}),(\d{1,2}),(\d{1,2})"

Set oMatchCollection = oRegex.Execute(rg.Formula)

Y = oMatchCollection(0).submatches(1)
M = oMatchCollection(0).submatches(2)
D = oMatchCollection(0).submatches(3)

GetDt = DateSerial(Y, M, D)

End Function
=========================================

The routine will return a #VALUE! error if there is no DATE function with
numeric arguments in cell_ref.

On the assumption that you might want to substitute cell references for those
arguments to the DATE function, I expanded the GetDt routine:

=========================================
Option Explicit

Function GetDt(rg As Range) As Date
Dim sFormula As String
Dim oRegex As Object
Dim oMatchCollection As Object
Dim YMD(1 To 3) As Integer
Dim i As Long
Dim Temp As Variant

sFormula = rg.Formula

Set oRegex = CreateObject("VBScript.RegExp")
oRegex.Pattern = "(\(DATE\()(.*?),(.*?),(.*?)\)"

Set oMatchCollection = oRegex.Execute(rg.Formula)

For i = 1 To 3
   Temp = oMatchCollection(0).submatches(i)
   
   If IsNumeric(Temp) Then
       YMD(i) = Temp
   Else
       YMD(i) = Range(Temp).Value
   End If
Next i

'Sanity Check

If YMD(1) < 1901 Or YMD(1) > 2200 Then
   GetDt = Error(xlValue)
   Exit Function
End If

GetDt = DateSerial(YMD(1), YMD(2), YMD(3))

End Function
==================================

This function should do what you want.  However, if the year is not in the
range of 1901-2200, it will give a #VALUE! error.

I chose 1901 for the earliest allowable year because there is a difference in
how Excel interprets dates, compared with VBA, prior to March 1, 1900.  This
could be handled in code, if necessary, but it probably isn't.

You can change the upper allowable year to anything up to 9999.

I did not check the values for month and day, as Excel will accept arguments
that are not in the range of 1-12; 1-31 -- merely doing the appropriate math to
change them to a valid date.  For example:

DATE(2000,-3,0) --> 31 AUG 1999

--ron