example.cs

public void DoStuff()
{
    SendData("https://blah", "blah").ContinueWith(task => DoEvenMoreStuff());
}

private async Task SendData(string url, string data)
{
    WebRequest req = WebRequest.Create(url);
    using (StreamWriter writer = new StreamWriter(await req.GetRequestStreamAsync())) // why await here?
    {
        writer.Write(data);
        writer.Close();
    }
    
    WebResponse resp = await req.GetResponseAsync(); // or here? we're already executing in the ThreadPool.
    DoOtherStuff(resp);
}