In bowl of stand mixer, beat sugar and butter on medium speed until light and fluffy, about 3 minutes. Beat in egg, egg yolk, orange zest and vanilla until well combined.
With the mixer on low speed, gradually add flour mixture to bowl, mixing until combined.
Turn dough out onto a work surface and divide into three equal pieces. Shape each piece into a flat disk. Wrap each disk tightly in plastic wrap. Refrigerate for at least 1 hour, until cold, or for up to 3 days.
Preheat oven to 350 degrees F, placing racks in the upper and lower thirds.
On a lightly floured work surface, roll out one disk of dough to a thickness of ¼ inch. Using cookie cutter, cut out shapes and carefully transfer them to 2 prepared cookie sheets, spacing them about 1 inch apart. Reroll scraps as necessary. Repeat process with more dough until both cookie sheets are full.
Bake for 11 – 15 minutes, switching positions of cookie sheets halfway through, until cookies are set and very lightly browned. Let cookies cool on cookie sheet for 10 minutes, then carefully transfer them to wire racks to cool completely before decorating.
Repeat steps 6 and 7 with the remaining dough.
Melt chocolate and milk in a double broiler. When cookies are cool, drizzle over the cookies and allow to set.