Preheat oven to 175 degrees celsius. Line a baking pan with parchment paper.
In a bowl, whisk together the flour, baking powder, and salt; set aside.
In a small bowl, combine the the sugar and orange zest, rubbing them together with your fingers until the zest is completely incorporated into the sugar.
Cream together the butter and the orange zest-infused sugar until light and fluffy, about 3 minutes. Add the egg and orange and mix until combined, scraping the sides of the bowl as needed. Gradually add the dry ingredients, mixing until just combined. If the dough seems a little on the soft side, refrigerate it for up to 30 minutes.
Scoop out the dough and roll them into balls, placing them 2 inches apart on the prepared cookie sheets. Bake for 10 to 12 minutes, or until very lightly browned around the edges, but still pale in the middle. Let cool for 5 to 10 minutes on the cookie sheet, and then remove to a cooling rack to cool completely.
Make the Sweet Orange Glaze: Whisk together the powdered sugar, orange zest, and enough orange juice to achieve the desired consistency (less juice for a thicker glaze, more for a thinner one). Spread glaze over top of the cooled cookies, and allow to set at room temperature for at least 30 minutes. Store at room temperature in an airtight container (divide layers with wax paper so the cookies don't stick together).
