Roughly chop the mint leaves and place in a medium-sized saucepan with the coconut milk. Turn the heat to medium. Stir occasionally and press on the mint leaves with the spoon to release the oils. Bring to a simmer.
Once simmering, add the honey and stir to combine. Turn off the heat and let the mint leaves steep for 30 minutes.
Pour the mixture through a fine sieve into a large bowl. Press down on the mint leaves to release any extra liquid into the bowl. Discard the leaves.
Add the peppermint extract and Greek yogurt to the bowl. Whisk to combine. Pour the mixture into a freezer-proof bowl (stainless steel works best) and place in the freezer.
Set a timer for 30 minutes. Stir the mixture every 30 minutes for 2 hours, scraping down the sides and whisking to combine.
Melt the chocolate with the coconut oil in the microwave for about 45 seconds. Drizzle over the partially frozen yogurt and whisk to break up the chocolate into little pieces.
Freeze overnight until solid.
minutes before serving, set the frozen yogurt on the counter to defrost until scoopable.
You can also serve this as soft serve if you begin preparation early in the day. The frozen yogurt freezes solid overnight but reaches a nice texture after defrosting, more like hard ice cream.