What was my first clue? Sitting down behind the wheel to discover it wet and sticky. Yes, folks, since I left it out in the sun all day, I left the driver's side window cracked open slightly. What appears to have been a rather good and/or lucky shot tagged the top of the door frame, sending about two-thirds of the egg (shell bits and all) splattering inside.
The exterior I can wash tomorrow with the car wash coupon I'd been saving (edit: after a quick Google search, I'm going to scrub it now, and hope the egg got thrown just a few hours ago rather than during the afternoon). But cleaning the entire front interior is going to be a bitch.