Configuration FileWithCredential {

    Import-DscResource -ModuleName PSDesiredStateConfiguration

    Node $AllNodes.NodeName {

        # copy files from a file share to a new folder on the target node
        File CopyFileShareFolder {
            Ensure = 'Present'
            Type = 'Directory'
            Recurse = $true
            SourcePath = '\filesharefoldersubfolderstuff_I_want_to_copy'
            DestinationPath = 'c:psDSCfilesharedestination'
            # If I use Credential instead of PsDscRunAsCredential, it works
            # Credential = Get-Credential -UserName ourdomainmyaccout -Message 'Enter Password'
            PsDscRunAsCredential = Get-Credential -UserName ourdomainmyaccout -Message 'Enter Password'
        }
    }
}

$ConfigData = @{
    AllNodes = @(
        @{
            NodeName = 'target-server'
            PsDscAllowDomainUser = $true
            PsDscAllowPlainTextPassword = $true
        }
    )
}

PS C:UsersmeDocumentspscodedsc_test2> FileWithCredential -ConfigurationData $ConfigData
PS C:UsersmeDocumentspscodedsc_test2> Start-DscConfiguration .FileWithCredential -Verbose -Wait -Force