Preheat the oven to 350°F. Line a baking sheet with parchment paper.
To make the dough: In the bowl of a stand mixer fitted with the paddle attachment, add the butter, cane sugar, light brown sugar, and peppermint extract. Mix on low until combined and there are no chunks of butter. Add the eggs and yogurt and mix just slightly, enough to break the yolk.
In a separate bowl, add the flour, cocoa, baking powder, and sea salt and whisk together. Add the flour mixture to the butter mixture and mix on low until a stiff dough forms.
Using your hands form a large log out of the cookie dough and flatten slightly so it’s about 1-inch thick, it should be about 13 x 3 inches.
Bake for 35 minutes or until the middle looks set, but not completely done. Remove from oven and let rest for 15 minutes. Trim off the edges, then slice into 12 pieces and bake again for 20 minutes. Allow to cool completely on the baking sheet.
To make the topping: Using a double boiler melt 80% of the milk chocolate. Once it reaches 110°F on a chocolate thermometer (find here), remove from heat and add in the remaining 20% and stir to combine completely. Allow the chocolate to sit until it reaches 91°F on a chocolate thermometer and is in the tempering stage. (You can skip tempering if you prefer and just melt doing 30 second intervals in the microwave).
Dip one side of each biscotti into the milk chocolate, place back on the baking sheet. You can also drizzle chocolate on top if you prefer. Repeat with the rest of the biscotti. Place baking sheet in fridge to set the chocolate for about 1 hour.
Store in a cool dry place, or in the fridge for up to 7 days.