Preheat the oven to 350°F and line a baking sheet with parchment paper.
In a bowl, whisk together the flour, cocoa powder, and baking soda.
In a separate bowl, cream the ¼ cup softened butter with the granulated sugar until light. Beat in the egg and vanilla extract.
Stir the dry ingredients into the wet mixture until a dough forms. Roll the dough into 8 small balls and flatten each into a 2-inch round on the baking sheet.
Bake for 8 to 10 minutes until the edges are set. Cool the cookies completely on a wire rack.
Melt the semisweet chocolate in a microwave-safe bowl in 30-second bursts, stirring until smooth. Dip the open end of each sugar cone into the chocolate and set aside to harden.
For the buttercream, beat the ½ cup softened butter until creamy. Gradually add the powdered sugar, then mix in the orange zest and orange juice until smooth.
Pipe a ring of orange buttercream around the center of each cooled cookie. Place one chocolate-dipped cone on top of the buttercream to form the hat.