You can extract data from the car using TeslaFi, various apps, or the Tesla API (if you care to write your own script). This information will not directly measure the power used by the EVSE, though, just the power consumed by the car. There will be some small losses between the two and perhaps other reasons for discrepancies. TeslaFi, at least, records both power stored in the battery and power taken in by the car, which enables it to calculate a charging efficiency. On rare occasions, this is over 100%, which is theoretically impossible, so clearly there's some measurement error. I seem to recall hearing that this is because the API provides a sum total for charge added to the battery (in kWh) but only minute-by-minute recording of the instantaneous power use (in kW), and TeslaFi sums the latter over time. If this is correct, then any API-based tool will be of limited accuracy in total power drawn from the wall.
Beyond that, you'd need to add or replace hardware. A simple electric meter (like the kind your house has to measure power used for billing by the utility) in-line with the EVSE will do the trick, but if you want per-charge-session data, you'd need to check it manually every time you unplug. Maybe there are WiFi-enabled networked meters that will help with this, but if so, I don't have references to them.
A similar option would be to replace the Tesla Wall Connector with a third-party EVSE with networking capabilities, like a JuiceBox, ChargePoint Home, or OpenEVSE. These devices can do exactly what you want, although you'd need to use Tesla's J1772 adapter with them. It might be possible to take components from one of these and add it to Tesla's Wall Connector to add WiFi capabilities, but I'm far from certain of that; certainly I've never heard of it being done.
There are also whole-house electricity monitoring tools available. I'm not very familiar with these products, but my understanding is that some of them can learn to identify specific devices because of their patterns of use. I'd expect an EVSE would be easy to identify because it draws so much power; however, there might be some slop (missed use) if the car draws less than its usual amount of current -- say if you turn on the cabin heat or AC shortly before you leave.