Make the crust: In the bowl of a stand mixer fitted with the paddle attachment, cream the sugar and butter until light and fluffy. Add the flour, milk and vanilla, and mix until a smooth dough comes together. Cover in plastic wrap and refrigerate for 30 minutes.
Meanwhile, prepare the filling: In a medium bowl, whisk together the sugar and butter until incorporated. Add the flour and eggs, and whisk until smooth. Whisk in the buttermilk, moonshine and nutmeg to incorporate, then set aside.
Make the blackberry-moonshine drizzle: In a small bowl, mash the blackberries with a fork until they fall apart. Stir in the remaining drizzle ingredients and set aside.
Roll the dough out, between 2 sheets of parchment paper dusted with confectioners' sugar, into a 12-inch circle. Transfer to a 9-inch pie dish and trim the excess, then crimp the edges. Transfer the pie dish to the freezer to freeze for 1 hour.
Preheat the oven to 350º. Remove the pie shell from the freezer and layer the blackberries in an even layer on the bottom. Pour in the filling and bake until lightly golden, 30 minutes. Cover with foil and continue to bake until the filling is set, 30 minutes more.
Let the pie cool completely, then slice and serve each slice with a spoon of the blackberry-moonshine drizzle over top.