Add the yogurt, milk, honey, vanilla and peppermint extract to a large bowl or pitcher. Whisk to incorporate all of the ingredients.
Drop 1 Tablespoon of the Andes chocolate chips into each popsicle mold.
Pour the yogurt into each popsicle mold, leaving a little room at the top to add an additional 1-2 Tablespoons of Mint chocolate chips (some will fall down into the middle of each pop).
Insert lids/sticks for each mold and freeze for at least 5 hours.
Once the popsicles are completely frozen, line a cookie sheet with wax or parchment paper. Run the popsicle molds under warm water for about 20 seconds and gently release. Place on the lined cookie sheet.
Microwave the mint chocolate candy melts for 45 seconds in a microwave safe bowl. Stir and continue to microwave in 10 second increments until completely melted and smooth.
Dip the tops of each popsicle into the melted chocolate and drizzle additional chocolate all over each popsicle. Immediately, sprinkle additional mint chips on the melted chocolate, if desired.