In most of the South, telling a person “how the cow ate the cabbage” means telling them the unvarnished truth even if it’s not pleasant.
The way I’ve heard it used by East Texans, though, is a little different. It’s more like telling someone off in no uncertain terms, in a way that leaves them no possible room for argument.
Telling someone how the cow ate the cabbage is about truth-telling, but it’s also about setting things right, addressing a behavior problem, maybe even giving someone a verbal cease-and-desist order and making sure they understand exactly why, and wouldn’t dare dispute it if they know what’s good for them.
All in all, it’s a charming, colorful term for some generally unpleasant truth-telling—or what the teller considers to be truth-telling. Generally it’s the teller who says, “I told him how the cow ate the cabbage,” not the person who was told off. It’s almost a brag.
In Texas it would be very unusual to hear someone say, either ruefully or humorously, “He told me how the cow ate the cabbage.” I guess maybe that tells you something about us.