Add coconut milk and honey to a medium saucepan over medium-low heat. Heat until hot and steaming, but not boiling, stirring occasionally. Remove from heat and add mint leaves. Stir to combine and let mint leaves steep for 15 to 30 minutes. Fish out the mint and discard.
Add minty coconut milk and spinach to a blender. Puree until spinach is completely broken down.
Pour into molds, leaving a little space at the top for them to expand. Insert sticks and freeze until hard (at least 4 hours).
Just before removing pops from the freezer, add chocolate to a heat-resistant bowl. Bring a pot of water to a boil and set the bowl of chocolate over the boiling water (just above the water, not submerged). Stir constantly until most of the chocolate is melted. Remove the bowl from over the steam and continue to stir until chocolate has all melted.
Remove pops from the freezer and run the mold under warm water for a few seconds to loosen them up. Remove each popsicle from the mold, drizzle with chocolate, and (if you like) sprinkle with a dash of finely chopped chocolate.