Cook time is really chill time. Make sure you use peppermint extract rather than mint extract since mint extract is usually spearmint. My husband prefers finely grated chocolate, but I like big chunks that melt in your mouth. To get that softer texture, you need to melt the chocolate and mix it with oil or coconut oil (not recommended with mint!) first, let it set, then chop it up and put it in at the end. This page will give you more information on how to do that. http://www.cookiemadness.net/2011/11/super-simple-mint-chocolate-chunk-ice-cream/
For fresh mint ice cream, start by putting 1 cup milk and 1 cup of the cream in a large saucepan along with about 20 mint leaves. Bring to a simmer, then turn off heat and let steep for 10 minutes. Push through a sieve, then follow recipe as directed using the mint flavored milk/cream mixture.