Can you charge an EV with an extension cord?

Yes.

I'm living proof that it can be done despite what the manufacturer instructions say, however like anything electrical, you need to be careful. Whether it's an extension cord or not, you will encounter problems if when the plug & socket you use isn't perfectly good.

The issue with car charging on a general purpose outlet (GPO) isn't that they're overloaded per se, it's just that you can be running at 80% of the rated capacity FOR SEVERAL HOURS STRAIGHT.

There's no diversity in the load, it's like running a kettle or a blow heater on high all the time. If the contacts in the GPO or the pins on the plug are a bit dirty, the poor connection will generate heat and melt the plug/socket.

This photo shows a GPO that has been discoloured by heat, and the plug, which you can see on the right pin, has begun to melt.

So far, I've had to replace 1 plug top, two cord extension sockets and 2 GPO wall plates over 5 years of charging a car with a standard EVSE. None of them has been what I would call a dangerous situation, I've just noticed the plugs were hot to the touch, and the plastic was soft and, as a result, discoloured or slightly deformed.

BE AWARE that whenever you use a plug-in car charger, you should turn the switch off at the wall before unplugging the cord. If the plug or socket has been damaged, the pins may be welded together. Whether it's still hot or not, the plastic could be melted enough that the plug comes apart in your hand, exposing live metal parts.

There are a few facts to consider about using an extension cord :

Household wiring normally uses 2.5mm² cable behind the GPO back to the switchboard.
Standard household extension cords are as little as 0.75mm²
So-called "heavy duty" extension cords sold at the shops are only 1.5mm²
These skinny or excessively long cords create loss and may overheat if they're coiled up.

EVSE with cord extension socket showing some heat generated.

The best way to approach EV charging

If you plan to use an extension cord, get an electrician to make one.
That way, you have shiny new contacts and a cord that's just the length you need
Specify 2.5mm² flexible cable (4mm² is difficult, if not impossible, to properly fit plug ends)
While you're at it, have the electrician install a new, good-quality GPO to use.
Apply some preservative such as Inox or the heavier Lanox to prevent corrosion.
It should go without saying that double adaptors and power boards should not be used at all.