MINI is geared toward custom orders, so there's a web site where you can track your order. There's also an automated phone system you can call and get even more up-to-date information. When I called it this evening, it said the car would be finished next Monday (6/25)!
Of course, that finished car will be in Oxford, England, so it will take a while to get to my local dealership. I'm told there are ways once you get the VIN number of tracking the ship it's on as it crosses the Atlantic. I will totally be doing that.