The quirk is that when you book a business class award, and add a connection in economy, sometimes the price of the award drops.
Even better you don’t need to do this as a throwaway ticket without checking bags. Alaska Airlines offers one-way awards with a free stopover. So book your business class ticket to Europe and add a one-way coach flight to another destination for later. You should do this anyway any time you’re booking an award since it’s a free extra trip. Except here it’s negative-priced.