The soap was overheating. The long oval darker center is where the soap is warm enough to be in the gel phase. When soap gets hot enough, it will expand and crack like this.
It's pretty common for soap makers to protest, "But I did everything exactly the same!" except the soap is clearly showing something was indeed not the same. And when we dig into the matter in more detail, it's clear there was a significant trigger for the problem
I can't say the use of milk alone is a reason for overheating, but you didn't provide a recipe nor any info on temperatures, so it's anyone's guess what the difference is.