All you used for color was cocoa powder? Maybe it's my screen, but your soap looks grey to me and not brown, so that's why I ask.
How did you mix your lye solution? Did you slowly add the dry lye to room temperature water? Did you use ice cubes to add the dry lye to? If the second, did you dump all the lye at once, or slowly add the dry lye to the ice cubes? Was the lye solution hot or warm or cool when you added it to the oils?
How did you melt your Coconut oil? Or was it already melted and at room temperature? (In the summer in my house, Coconut Oil melts at room temperature.) Did you melt the coconut oil using the lye as the melting agent (called the heat transfer method)? Did you mix/blend all the oils together before adding the lye solution?
How did you mix the lye and oils? Did you use a stick blender/hand-held blender? Did you stir by hand?
Were the oils and lye solution both close to the same temperature as each other? Or was the lye solution super hot when you poured it into the oils, while the oils were not heated? I am getting at were the temps close or was there a huge difference in the temperatures of the two? Did you add the lye solution to melted oils slowly? Did you dump the lye solution all in at once?
How did you mix the cocoa into the batter? Did you pre-mix it in some water or oil from the recipe? And when did you add the cocoa? Did you plan on getting a uniform color distribution? Or did you plan a color variation?
How fast did the soap trace (thicken)? Did it thicken up really fast after adding the lye? Or was it slow to thicken?
All those things can impact how thoroughly the lye mixes into the oils for a well mixed soap batter.
I can't really tell from your picture if those are lye pockets, but I suspect that your mixing method did not evenly distribute all the color. And if you planned on a uniform color and didn't get it, perhaps your mixing method also was an issue for the lye and oils and you could have lye pockets. Or it could just be from mixing the colorant into the soap batter too late in the process.
As far as how peppermint oil reacts with a soap batter at different stages, I don't know. Hopefully someone who does will respond if that could have an impact. I do know some fragrances/essential oils can cause soap batter to rice.
When did you add the essential oil?
