The good news...
Fundamentally, the functionality that you are looking for is exactly what every production EV with fast DC charging has... minus the onboard charger which isn't used for DC charging (it converts AC at the utility voltage to DC regulated to the desired battery voltage, and that will be done by the off-board DC charger). You don't even need it to be particularly fast.
The bad news:
There are multiple fast DC charging standards. Of course you wouldn't want to try any of Tesla's Supercharger standards without a Tesla car, but there's also CHAdeMO (possible to implement DIY, but falling out of favour), and CCS (difficult to implement DIY). While fast chargers are commercially available from many suppliers, they are rarely installed in homes so there is a lack of reasonably priced and readily available choices... and you would probably have to adapt something from a production EV for the part in the car.
The initially suggested idea of just using a common on-board charger, but placed offboard and connected with any connector capable of safely handling the current and voltage, is probably the easiest, although it would tie you to using only your specific hardware instead of public charging stations. If you use a standard connector but don't implement all of the proper signalling, you would be able to plug into a charging station using that connector but it won't turn on.
The only certified production battery-electric aircraft - from Pipistrel - has the same situation... they don't want to carry the weight and bulk of an on-board charger, and always return to the same base so they can have a dedicated charger there. They used some proprietary connector at first, and are now using (on the type-certified Velis Electro) a connector and standard specific to aircraft (SAE AS6968, from SAE committee AE-7D), so clearly there is not a single easy solution that everyone will agree on for a race car.
Formula E cars might be a good example, but they use some sort of custom plug and system from Enel X, and are likely changing it anyway as they introduce in-race charging (which will be very high rate, such as 600 kW, versus the current 80 kW between-race charging).