To a stand mixer with the paddle attachment, add butter and sugar. Mix on medium speed for about 2 minutes.
Reduce the mixer speed to low and add in egg, milk, and vanilla. Mix for about 30 seconds to incorporate. Then, turn the mixer to medium-high and blend until light and fluffy.
In a separate bowl, sift cocoa, flour, baking soda, and salt. With the mixer on low, add the flour mixture to the sugar mixture and beat until just combined.
Remove the mixer bowl from the stand. Cover and refrigerate the dough for about an hour.
When ready, preheat the oven to 375°F and line 2 large baking sheets with parchment paper. Set aside.
Using a 2-tablespoon scoop, place dough on the lined baking sheet. Roll each scoop of dough into about a 1-inch ball.
Pour remaining sugar onto small plate or bowl.
Roll each dough ball in the sugar and place it on the lined baking sheets about 2 inches apart.
Bake for 10 minutes, or until set.
Remove the cookies from the oven and let them cool for about 10 minutes before adding the filling. While the cookies are cooling, make the filling.