^^ I don't doubt that is a nice solution, but it might be an expensive one. It also presumes that his electrical panel can support the load without an upgrade.
OP will have to balance cost with desired charging speed
His current 30 Amp circuit supports ~ 5 kW charging as is -- about 20 miles of EV range an hour. That is almost certainly well within his car usage demands so he should understand that nothing is forcing him to upgrade the wiring (and perhaps more). He has a choice.
If he decides to keep his wiring, he will either use the EVSE he already has or buy another, but one way or another the EVSE will be max rated for a 30 Amp breaker and have a 3 prong plug*. I gather that dryer circuits are two hot wires and a neutral. Since the EVSE plug is two hot wires and a ground wire, that will have to be resolved
- I've read that some 14-30 EVSE play games with the neutral and ground, sometimes leaving the neutral prong unconnected; at other times tying the neutral and ground together. This is above my pay grade, other than realizing that the circuit has to be consistent, meaning that the connections in the panel match the plug. The underlying gotcha here is that 10-30 is a legacy standard that is not allowed for new installations. So no EVSE 10-30 plugs, and a requirement to use the non-energized wire as a ground in 3 wire circuits where EV charging is concerned.
2013 LEAF 'S' Model with QC & rear-view camera
Bought Jan 2017 from N. California
Two years in Colorado, now in NM
03/18: 58 Ahr, 28k miles
11/18: 56.16 Ahr, 30k miles
09/20: 54.3 Ahr; 38k miles
2018 Tesla Model 3 LR, Delivered 6/2018