In the large bowl of a stand mixer, combine room temperature butter (cold butter won't work here!) and confectioner sugar. Beat together until completely creamed together (you may need to scrap the sides of the bowl a few times).
Add in the orange extract, orange zest, and juiced orange. Beat again until smooth.
Pour in the all purpose flour and salt. Mix again until dough forms.
Fold in the chopped dried cranberries. Spin the mixer 4-6 times to disperse the cranberries, but be careful not to overmix.
Lay a large piece of plastic wrap on your work surface. Remove the dough from the mixer. It should have enough form that it stays together in one lump, and it shouldn't be too sticky or crumbly (see FAQs if your dough doesn’t seem quite right).
Use your hands to form dough into a log shape roughly 2-3” in diameter. **If you'd like to make 18-24 cookies, make the log more narrow. Note: this will effect bake time. Monitor closely.
Fold the plastic wrap tightly around the log and place in the refrigerator for at least 4 hours or overnight.
Preheat the oven to 350°F. After the dough is completely chilled, remove from the plastic wrap. Use a straight sharp knife to cut even cookies, roughly ¼” thick.
Place cookie dough rounds on a cookie sheet lined with a piece of parchment paper and top with a sprinkle of cane sugar. Bake cookies for 9-12 minutes or until centers are firm (the shortbread cookie will change colors from a yellow to more of a white when baked. You will know they are done when there is any hint of golden brown on the baked cookies' bottom edges). Keep a close eye as bake time will vary from oven to oven.
While the cookies are baking, make the glaze: Combine orange juice, milk, and powdered sugar in the stand mixer. Whisk together until a thick, citrus glaze is formed. Note: If the glaze seems too thick, add milk in 1 tsp increments until desired consistency is reached. Avoid adding too much liquid, because if it is too thin the glaze will not harden on the shortbread cookie.
Once the cookies cool, use a spoon to add ½ tbsp of icing onto each cookie. You can also opt to drizzle the glaze if you wish. Garnish with fresh orange zest and/or more chopped cranberries.