I've seen people run chargers off of their dryer outlet, but I doubt running a separate outlet off that same circuit would be to code. A dryer outlet is a dedicated 50A 220V circuit because a dryer needs 50A @ 220V, same with an EV. When you unplug the dryer and plug in your car you can't run the dryer at the same time. Have a second plug installed on the same circuit and you could *try* to charge the car while someone else *tries* to dry clothes. I say try because the load would cause the breaker to trip.
As part of my basement project I ran a dedicated 50A 220V GFCI protected outlet from my main panel to the garage. It had to be GFCI protected because it is in a garage, same if it was outside if you didn't have a garage. I don't have an EV yet, but I suspect I will, or certainly the next owner will.