A quick Azure Function will also drain it, can run it locally or publish it so its always being cleared.

[FunctionName(FunctionName)]
public async Task Run(
[ServiceBusTrigger("my-q/$DeadLetterQueue", Connection = ConnectionAppSettingName)]
Message serviceBusMessage,
CancellationToken cancellationToken)
{
this.Logger?.LogInformation("Completed message from dead-letter queue.");
}