We can use PowerShell to search through the event logs of a machine object ($objVM in the example below) for events which match a specific pattern - in this case powering off a machine. Once we have the event object, we can access the properties of the first object in the array (the most recent event).

$objEvent = @(
    Get-VIEvent -Entity $objVM | Where-Object {$_.fullFormattedMessage -like "Task: Power off Virtual Machine"}
$objEvent[0].userName $objEvent[0].createdTime

I recall seeing an alternate way of getting events, which might be faster; if I have time, I’ll look it up.