Combine the flour, sugar, vanilla extract, orange zest and salt in a food processor; pulse to lightly mix. Add the butter and pulse until combined. Form the dough into a disk and wrap in plastic. Chill for 30 minutes.
Preheat the oven to 350 degrees F.
On a lightly floured work surface, roll the cookie dough out to a 1/4-inch thickness. Cut out cookies using a 1 1/2-inch round cutter. Arrange the cookies, spaced at least 1-inch apart, on a parchment-lined baking sheet.
Bake until the cookies are a pale golden brown, about 15 minutes, rotating halfway through. Let cool slightly, then transfer the cookies to a wire rack to cool completely.
Heat an inch of water in a small saucepot. Place the chocolate in a heatproof bowl and set it over the saucepot. Bring the water to a simmer. When the chocolate has melted, immediately remove the bowl from the saucepot and whisk the chocolate until smooth. Dip the cookies halfway into the chocolate and place them on parchment paper to set. Once the chocolate has set, enjoy.