Out-File seems to force the BOM when using UTF-8:
$MyFile = Get-Content $MyPath
$MyFile | Out-File -Encoding "UTF8" $MyPath
How can I write a file in UTF-8 with no BOM using PowerShell?
Update 2021
PowerShell has changed a bit since I wrote this question 10 years ago. Check multiple answers below, they have a lot of good information!