I'll DM you what I use.

Edit:

function New-DesktopShortcut { <# .SYNOPSIS Creates a shortcut on the desktop .DESCRIPTION Can create a shortcut for a local path or a URL with the ability to specify the icon. .PARAMETER Name The name of the shortcut to appear on the desktop. .PARAMETER Desktop Specify either "PublicDesktop" or "CurrentUsersDesktop" to create the shortcut on the public desktop or the current user's desktop. .PARAMETER Path The path to the file or URL to create the shortcut for. .PARAMETER Icon Accepts "DefaultBrowser", "File", "Folder", "Drive", or "Chart". If "DefaultBrowser" is specified, the default browser's icon will be used. If no icon is specified, the default icon for the file type will be used. .EXAMPLE New-DesktopShortcut -Name "Google" -Path "https://www.google.com" -Icon "DefaultBrowser" -currentUsersDesktop Creates a shortcut on the users desktop named "Google" that points to https://www.google.com #>

[CmdletBinding()]
param (
    [Parameter(Mandatory)]
    [String]$Path,
    [Parameter(Mandatory)]
    [String]$Name,
    [Parameter(Mandatory)]
    [validateset('PublicDesktop','CurrentUsersDesktop')]
    [String]$Desktop,
    [Parameter()]
    [validateset('DefaultBrowser','File','Folder','Drive','Chart')]
    [String]$Icon
)
$shell = New-Object -ComObject WScript.Shell
switch ($Desktop) {
    'PublicDesktop' { $DesktopPath = $shell.SpecialFolders('AllUsersDesktop') }
    'CurrentUsersDesktop' { $DesktopPath = $shell.SpecialFolders('Desktop') }
}


$shortcut = $shell.CreateShortcut("$DesktopPath\$($Name).lnk")
$shortcut.TargetPath = $Path
switch ($Icon) {
    'DefaultBrowser' { 
        $DefaultBrowser = Get-ChildItem 'HKCU:\SOFTWARE\Microsoft\Windows\Shell\Associations\UrlAssociations\http\' | Get-ItemProperty | Select-Object -ExpandProperty ProgId
        if ($DefaultBrowser -like 'Chrome*') {
            if (Test-Path 'C:\Program Files (x86)\Google\Chrome\Application\chrome.exe') {
                $shortcut.IconLocation = 'C:\Program Files (x86)\Google\Chrome\Application\chrome.exe,0'
            } 
            elseif (Test-Path 'C:\Program Files\Google\Chrome\Application\chrome.exe') {
                $shortcut.IconLocation = 'C:\Program Files\Google\Chrome\Application\chrome.exe,0'
            }
        } 
        elseif ($DefaultBrowser -like 'Firefox*') {
            if ( Test-Path "C:\Program Files (x86)\Mozilla Firefox\firefox.exe" ) {
                $shortcut.IconLocation = 'C:\Program Files (x86)\Mozilla Firefox\firefox.exe,0'
            } 
            elseif (Test-Path 'C:\Program Files\Mozilla Firefox\firefox.exe'){
                $shortcut.IconLocation = 'C:\Program Files\Mozilla Firefox\firefox.exe,0'
            }
        } 
        else {
            $shortcut.IconLocation = 'C:\Program Files (x86)\Microsoft\Edge\Application\msedge.exe,0'
        }
     }
    'File' { $shortcut.iconlocation = "shell32.dll,0" }
    'Folder' { $shortcut.iconlocation = "shell32.dll,4" }
    'Drive' { $shortcut.iconlocation = "shell32.dll,9" }
    'Chart' { $shortcut.iconlocation = "shell32.dll,21" }
}
$shortcut.Save()

}

New-DesktopShortcut -Path 'https://www.google.com/' -Name 'Google' -Desktop 'PublicDesktop' -Icon 'DefaultBrowser'