You'd have to find the key used, which would be hidden inside of the browser's memory (and possibly hard to get out). Wireshark will do that for you, but it's not ideal.
A more usable way is: Set up a proxy on your system that decrypts and re-encrypts all SSL traffic - effectively acting as the browser. It re-encrypts with its own (auto generated) key, but you've put it's signing key in your truststore so your browser doesn't care. In the middle, you can see what's going on using Wireshark.
It's what most corporate firewalls do, as well as that Lenovo software etc.
A more usable way is: Set up a proxy on your system that decrypts and re-encrypts all SSL traffic - effectively acting as the browser. It re-encrypts with its own (auto generated) key, but you've put it's signing key in your truststore so your browser doesn't care. In the middle, you can see what's going on using Wireshark.
It's what most corporate firewalls do, as well as that Lenovo software etc.