Since you're calling from PowerShell, the best option is to pass a script block to powershell.exe, the Windows PowerShell CLI.
- However, this raises the question: why do you need to call the CLI from PowerShell to begin with, given that you could just call your Copy-Itemcommand directly, without the overhead (and potential loss of type fidelity) that comes with creating another PowerShell session, via a child process.
if you still need to call the PowerShell CLI from PowerShell itself, use the following:
$today = (Get-Date).ToString('dd_MM_yyyy_HH_mm')
powershell -Command { 
  Copy-Item -Recurse 'C:\ABC' -Destination ('C:\ABC_' + $args[0]) 
} -args $today
As for what you tried:
Removing the " around $today in 'C:\ABC_"$today"' would have worked too - the outer "..." quoting would still have ensured that $today is expanded.
- What you thought of as a single string argument,
- "Copy-Item -Recurse 'C:\ABC' -Destination 'C:\ABC_"$today"'", was passed as two arguments:
 - 
- Argument 1: Verbatim - Copy-Item -Recurse 'C:\ABC' -Destination 'C:\ABC_, which, due to being a (double-)quoted token became its own argument - despite other characters immediately following it.
 
- Argument 2: The value of - $today, immediately followed by a verbatim- '(the value of- "'"), e.g., verbatim- 06_2021_11_05'
 
- Not being able to compose a single argument from a mix of quoted and unquoted tokens if the first token happens to be quoted is a notable pitfall, discussed in detail in this answer. 
 
- When you use - -Commandand pass multiple arguments, PowerShell simply joins those arguments to form a single string by placing a space between them, before interpreting the resulting string as PowerShell code.
 - 
- Therefore, your two verbatim arguments, Copy-Item -Recurse 'C:\ABC' -Destination 'C:\ABC_and (e.g.)06_2021_11_05'were ultimately interpreted as
 Copy-Item -Recurse 'C:\ABC' -Destination 'C:\ABC_ 06_2021_11_05'- note the unwanted space.
 
See this answer for a comprehensive overview of the PowerShell CLI (covers both powershell.exe and pwsh).