Make the rosemary shortbread: Preheat the oven to 325°F (160°C). Line an 8-inch or 9-inch square baking dish (preferably aluminum) with parchment paper. Grease with nonstick spray, if you have.
Add the flour, sugar, rosemary, salt, and orange zest to the bowl of a food processor and pulse a few times to incorporate. Add the butter and pulse until pebbly and the butter chunks are no larger than the size of peas, about 20 pulses.
Transfer the dough to the prepared baking dish and press down with your hands or a flat-bottomed measuring cup to compact into an even layer, ensuring the dough reaches all the corners and edges of the pan. It will be crumbly, but will come together as it bakes.
Bake the shortbread for 40–45 minutes if using an 8-inch pan, or 35–40 minutes if using a 9-inch pan, until the edges are light golden brown. Remove from the oven. The dough will be a bit crumbly and unset, so let cool for 20–30 minutes.
After cooling slightly, lift the whole shortbread up out of the pan using the parchment paper and set it on a cutting board. Slice into 18–24 bars with a sharp knife, then carefully lift the parchment again to transfer the bars back into the pan to cool completely, 1–2 hours. The cooled shortbread can be wrapped in plastic wrap and kept in a cool, dry place for up to 2 days.
Make the pink peppercorn glaze: Using a spice grinder or a coffee grinder, grind the pink peppercorns into a fine powder.
Add the ground peppercorns to a small bowl, add the powdered sugar and salt, and use a small whisk to combine. Add the milk and continue to whisk until smooth. Add a bit more powdered sugar if the glaze is too thin.
Once the shortbread has cooled completely, remove the bars from the pan and set on a wire rack, spacing about 1 inch apart from one another. Place a baking sheet underneath the rack to catch any frosting drips, if desired..
Transfer the pink peppercorn glaze to a piping bag, then snip off the tip. Pipe the glaze back and forth across the shortbread cookies. (You could also use a spoon here, instead of a piping bag.) Let the glaze set for at least 30 minutes before serving.
Glazed shortbread cookies will keep in an airtight container at room temperature for up to 2 days.