UPDATE 9/9/2015 2:30 PM: This appears to be dead. Google Fights is still showing these discounted fares, but after selecting flights it shows regular fares. I couldn’t find the discount fares on ITA Matrix either. Please let me know if you see a route that is still valid at the sub-$2K rate.
OneWorld carriers such as American Airlines, British Airways, Iberia and others are currently offering amazingly cheap business class fares from the US to Europe on many routes. To check routes of interest, I recommend using Google Flights. Set the class of service selection to “Business”. Try various routes of interest and click the calendar icon to see available fares. Look for fares under $2,000.
Incredibly, many of this great prices are available as late as July 2016!
Here are a few example destinations worth searching:
Hat Tip: The Points Guy