1. I know your daughter is late, but before you go off half-cocked, give her a chance to tell you her side of the story.
2. Dick thought up a scheme to get rich quick, but he didn’t put much planning into it. He went off half-cocked, got into financial trouble, and made a fool of himself.

The expression probably originates from the idea of a gun misfiring when it is only half-cocked (as opposed to fully cocked), and therefore not fully ready to be fired.