Prep. Preheat the oven to 350˚F. Line two baking sheets with parchment paper and set aside.
Combine the wet ingredients. Whisk the eggs in a large bowl; add the sugar and whisk to combine. Whisk in milk, butter, and vanilla until smooth.
Combine the dry ingredients. In a separate bowl, whisk together the flour, baking powder, and salt.
Combine the ingredients. With an electric mixer on low, add the flour mixture to the egg mixture one tablespoon at a time; continue to mix until thoroughly incorporated.
Chill the dough. Remove the mixing bowl from the mixer and put it in the fridge for 15 minutes.
Shape the cookies. Remove the mixing bowl from the fridge. Lightly grease your hands with cooking spray, pinch off a little dough, and form into small balls about 1 inch in size.
Bake. Place the cookie balls on the baking sheets and bake for 12 to 15 minutes or until lightly browned on the bottom.
Let them cool. Remove from oven and let them rest on a cooling rack for 8 to 10 minutes or until cool enough to handle.
Spoon out a well in the cookies. Using a sharp paring knife, carefully cut out the bottoms of each cookie and make a well in the center of the cookie to fit the filling. Reserve the cookie crumbs in a mixing bowl.
For the Filling
Make the filling. In the bowl with the cookie crumbs, add the Nutella and milk; mix until thoroughly combined. If needed, add more milk for a creamier mixture.
Fill the cookies. Spoon the Nutella mixture into the wells, then sandwich two cookies together. Try to match cookies that are similar in size and shape for the best fit.
For the Food Colors and Garnish
Prepare the liqueur and food colors. Place half of the peach liqueur in one small bowl and the rest of the liqueur in another small bowl. Drop a few drops of red food color in one of the bowls with the liqueur, and yellow food color in the other.
Color the cookies. Dip one side of the cookie in red food coloring and the other side in yellow. Let them rest on a sheet of wax paper for 5 minutes before adding the sugar. I dip about five cookies in the colors and then go back to the first one and sprinkle it with sugar. You can also roll them in the sugar.
Finish and serve. Place the finished cookies on a sheet of wax paper to dry, then continue working with the rest of the cookies. Once the cookies are dry, insert a couple of mint leaves in each prepared cookie and transfer them to a cookie tray.
Notes
Chill: I let the cookie dough rest anywhere from 15 minutes to 2 hours before baking. The longer chill time helps the cookies puff up more.
Sticky Dough: I recommend using cooking spray on your hands to make it easier to roll the cookie dough balls.
Drying the Cookies: Once dipped, the cookies should dry out on wax paper uncovered for 5 minutes before adding the sugar. This step ensures that the sugar sticks rather than dissolves.
Storage: Cookies freeze well individually after baking and are completely cooled, but not if they are filled and decorated. Completely prepared cookies will keep in the fridge for up to 7 days, in a cool, dark room for 3 to 4 days, and on the counter for about 2 days.