In a large mixing bowl, cream together the butter and powdered sugar until light and fluffy, about 2-3 minutes.
Add the orange zest and vanilla and beat again.
Add the flour in 2-3 smaller additions, mixing well after each.
Add the cranberries and mix to combine.
Divide the dough into two equal portions, then roll each portion into a 2 inch diameter cylinder.
Place the coarse sugar on a plate or in a shallow bowl and roll the dough logs in the sugar to coat the outside. Wrap in plastic wrap and refrigerate for 2 hours.
Preheat the oven to 350°F (180°C), or 160°C if using a fan oven. Line two baking sheets with parchment and set aside.
Slice the cookies into ½ inch thick slices, and place cut side down on the prepared baking sheets. You should get about 15 cookies per dough log.
Sprinkle with remaining coarse sugar, then bake for 10-12 minutes, or until the cookies are lightly golden and no longer glossy on top.
Allow to cool for 5 minutes before transferring to a wire rack to cool completely.
Notes
Make sure that your butter is softened to room temperature. It's best to let this happen naturally, as microwaving butter could cause it to melt or become too soft.
Cream the butter and sugar together very well. You want the sugar to dissolve completely into the butter.
Avoid Overmixing: If you overmix the dough, your cookies will become tough. Once you add the flour, mix only until just combined.
Be sure to chill: The dough must be chilled in a log before you try to bake with it. If you skip this step, the cookies will spread too much in the oven
To Store: You can store baked cookies for up to 1 week at room temperature or 3 months in the freezer. Unbaked dough can be kept in the fridge for up to 3 days or frozen for up to 3 months.