I'm posting this so that the code is available to whomever finds it helpful.
Slightly reduced code based on Noctis's suggestion.
StringBuilder DescriptionText = new StringBuilder();
async void RunDescription(StringBuilder description)
{
DescriptionText = description;
await Task.Delay(1000); // Short delay before the text starts printing so the window has time to load
new Thread(AddTextToTextBlock).Start();
}
void TextBlockDispatcher(string text)
{
TextBlock1.Dispatcher.BeginInvoke(DispatcherPriority.Normal, new Action(() => TextBlock1.Inlines.Add(text)));
}
void AddTextToTextBlock()
{
foreach (char c in DescriptionText.ToString())
{
Thread.Sleep(30);
TextBlockDispatcher(c.ToString());
}
}