Preheat the oven to 350°F and line baking sheets with parchment paper. NOTE: I found that darker baking sheets work best for this recipe—when I tested this cookie on lighter aluminum sheets they spread a bit and stuck to the parchment.
In a large bowl, cream together sugar, butter, orange zest, and vanilla until light and fluffy.
Beat in eggs and orange juice
In a separate bowl, whisk together the flour, baking powder, and salt. Add to the creamed mixture and mix until just combined.
Stir in the walnuts.
Cover and refrigerate dough for at least 3–4 hours, or overnight. The dough will be pretty sticky—chilling helps it firm up for easier handling.
Drop dough by rounded teaspoons (about 1-inch balls) onto prepared sheets.
Bake 8–10 minutes, until cookies are set, spring back when touched (like a cake) and lightly browned on the bottoms. Tops should remain pale.
While cookies cool, make the glaze: whisk together powdered sugar, orange juice, orange zest, vanilla, and salt. Adjust with more sugar or juice to achieve a consistency that will cling to the cookies without running off.
Dip cooled cookies into glaze and let set until hardened.
Store in an airtight container at room temperature.