Make the chocolate ganache: place 2 cups milk chocolate chips in a medium heatproof bowl. In a small saucepan, heat 1 1/4 cups heavy cream over low heat until it just starts to bubble around the edges. Pour the hot cream over the chocolate chips, let sit 30 seconds, then whisk until smooth. Stir in 1/2 teaspoon vanilla extract and 1/4 teaspoon peppermint extract. Cover and refrigerate until thick and spreadable, stirring occasionally; this may take several hours or overnight. (The ganache will be more of a glaze and will not harden like a firm ganache.)
Preheat the oven to 350°F. Line a 10×15" jelly roll pan with foil and spray the foil with nonstick cooking spray.
In a large bowl, beat 3 eggs on high speed with an electric mixer for 3 minutes, until frothy and pale.
With the mixer running, add 3/4 cup granulated sugar, 2 teaspoons brewed coffee or water, and 1 teaspoon vanilla extract; beat until combined.
In a separate bowl, whisk together 1/4 cup unsweetened cocoa powder, 1/4 teaspoon salt, 1 teaspoon baking powder, and 3/4 cup all-purpose flour.
Gently fold the dry ingredients into the egg mixture just until blended. Do not overmix.
Spread the batter evenly in the prepared pan. The batter will be a very thin layer—use a spatula to spread it to all corners.
Bake 9–11 minutes, until the cake springs back lightly when touched.
While the cake bakes, lay a clean kitchen towel flat on your work surface and dust it generously with powdered sugar (for dusting).
As soon as the cake comes out of the oven, carefully invert the cake onto the powdered-sugar-dusted towel and remove the foil. Starting at a short end, fold the towel edge over the cake and roll the cake and towel together tightly into a log.
Let the rolled cake cool completely while rolled, at least 1 hour.
Make the filling: in the bowl of an electric mixer fitted with the whisk attachment, beat 1 cup heavy whipping cream on medium-high speed. Gradually add 4 tablespoons powdered sugar, about 1 tablespoon at a time, until the cream begins to hold soft peaks.
Add 1/2 teaspoon peppermint extract to the whipped cream, taste, and if desired add up to 1/4 teaspoon more (total up to 3/4 teaspoon) to reach your preferred mint intensity. Add 6 drops green food coloring and whisk briefly to combine.
Fold 1/3 cup mini chocolate chips or Andes Baking Chips into the green whipped cream filling.
Carefully unroll the cooled cake and peel off the towel. Spread the filling evenly over the cake, leaving a 1-inch border free of filling at both short ends.
Sprinkle the filling with additional mini chocolate chips if desired, then re-roll the cake (without the towel) tightly but gently. Wrap the rolled cake in plastic wrap and chill at least 1 hour to set.
Place the chilled cake roll on a wire rack set over a cookie sheet or tray. Remove plastic wrap. Pour the chilled ganache evenly over the cake, making sure to cover the top and sides.
Sprinkle 1/4 cup mini chocolate chips or Andes Baking Chips over the ganache for garnish.
Chill the frosted cake for at least 1 hour before serving. Store leftovers loosely covered in the refrigerator.