Step 1: In a large bowl, cream together the softened butter and powdered sugar until light and fluffy.
Step 2: Stir in the orange zest and vanilla extract until well combined.
Step 3: Sift the flour, cocoa powder, and salt into the butter mixture. Mix on low speed until a soft dough forms.
Step 4: Divide the dough in half and roll each portion into a log about 2 inches in diameter. Wrap in plastic wrap and chill for at least 2 hours.
Step 5: Preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper.
Step 6: Slice the chilled dough logs into 1/2-inch thick rounds and place them on the prepared baking sheet.
Step 7: Bake for 10-12 minutes until the edges are set. Allow the chocolate orange shortbread cookies to cool completely on a wire rack.