You run an "RSA signing server" that accepts connections only from the internal IP of your webserver (or maybe only TLS connections from across the internet but only if the client connecting to it has a client certificate signed by your own self-signed CA, but that depends on topology).

It runs a very simple app that accepts requests to sign something and responds with the <something> signed by your RSA private key. The code for this is very minimal and secure. You teach your web server to use this thing during TLS handshake, to sign the ephemeral key exchange.

If the web server is hacked, the hackers gain the ability to sign things with your private key, but they don't get the private key itself. They need to hack the "RSA signing service" server for that. They can't stockpile signed ephemeral key exchanges. After you detect the hack, snapshot and kill the hacked server, start a new one from clean backup, they lose the ability to impersonate your site.

CloudFlare have a writeup on their service that does this (TLS negotiation by their TLS terminator with only you holding the key): https://blog.cloudflare.com/keyless-ssl-the-nitty-gritty-tec...

BTW, you can store private keys in a HSM on your private key server and that's an additional layer of protection, but nobody uses TLS accelerator cards anymore that I'm aware of. You can simply do the relevant crypto on commodity CPUs and still have plenty of throughput.