Preheat the oven to 180°C fan-forced. Line two baking trays with parchment paper and set aside so the biscuits bake evenly and release easily.
In a large bowl, beat the softened butter and brown sugar until pale and fluffy, about 2 to 3 minutes with an electric mixer. The mixture should look light and slightly whipped.
Beat in the vanilla extract. Add the plain flour, desiccated coconut, bicarbonate of soda, and milk. Mix until a soft dough forms. If the dough feels sticky, add flour 1 tablespoon at a time until workable.
Roll teaspoon sized portions of dough into balls and place them on the trays with space between each one. Gently flatten with a fork, creating light ridges without cracking the surface.
Bake for 12 to 14 minutes, until lightly golden around the edges and set but still soft. Transfer to a wire rack and cool completely before filling.
For the filling, beat the butter until pale and creamy. Gradually add the icing sugar and cocoa powder, mixing slowly at first. Add the milk and vanilla extract, then beat until light, smooth, and spreadable.
Spread or pipe the chocolate filling onto the flat side of one biscuit, top with another biscuit, and press gently to sandwich. Repeat with the remaining biscuits.