First get the subscriptions you want to assign permissions on:
$subs = Get-AzSubscription |? { $_.Name.Contains("NorthAmerica") }
Then get the client id of the identity you to assign permissions for:
$id = Get-AzUserAssignedIdentity -ResourceGroupName my-shared-prod-westus2 `
-Name my-shared-prod-westus2-id
Now perform the actual permissions assignment:
$subs |% { New-AzRoleAssignment -Scope "/subscriptions/$($_.Id)" `
-RoleDefinitionName "Contributor" `
-ApplicationId $id.ClientId }
That’s it, folks!
Alexander Batishchev's Blog 