Internal Double Crux (IDC) is a tool for resolving conflict in one's mind. It's a script for focusing on two conflicting inner voices and holding space for them to debate and compromise. A sort of internal couples therapy, if you will. It's built on the notion of double crux, which is a tool for resolving disagreements between two people, but in this situation applied to the inside of one's own mind as though it is made up of many smaller people. IDC was developed by staff at the Center for Applied Rationality.
For those who find formal instructions helpful, these are the four instructions that CFAR staff give to attendees.
The current best writeups are in the CFAR Handbook and in Alkjash's Hammertime sequence.
For a similar technique that IDC is arguably a special case of, see Internal Family Systems.