Whisk the flour, cocoa powder, baking soda, and salt together in a medium bowl.
In a stand mixer fitted with a paddle attachment, beat the butter, brown sugar and 67g granulated sugar together on medium-high speed until smooth and creamy. Add the egg, vanilla extract and beat on high speed until combined. Pour the dry ingredients into the wet ingredients, add the milk, and mix on low until combined.
Roll balls of dough, a little less than 1 Tablespoon each, and roll each into remaining granulated sugar. Place dough balls onto a lined baking sheet. Using the end of a spatula, make an indent into each cookie.
Chill the shaped cookies for at least 2 hours in the refrigerator.
Preheat oven to 350°F/180°C. Line a baking sheet with parchment paper. Remove chilled and shaped cookies from the refrigerator. Space the cookies about 2-3 inches apart.
Bake for 12-14 minutes. Remove from the oven. The indents will have lost some shape so use the end of a spatula to make an indent again into the warm cookies.
Allow cookies to cool on the baking sheets for 5 minutes, then transfer to a wire rack to cool completely before filling with ganache.
Place white chocolate in a heat proof bowl.
Bring cream to the boil in a small saucepan, then pour over white chocolate. Let sit for 3 minutes, then whisk until smooth. Refrigerate, stirring occasionally, for about 30 minutes.
Using a piping bag, fill each cookie with the ganache.