While that is cooling, cut two limes in to eighths so that they are easy to muddle. I always like to cut them into eights rather than quarters because it expresses the juice easier and I tend to smack my knuckles on the cup rim less because I can apply less aggressive pressure. Place the cut limes, simple syrup, lime essential oil, and peppermint essential oi (or leaves) into a tumbler and muddle until the limes are well crushed and the juice is expressed.