Place the butter and confectioners sugar in the bowl of a stand mixer. Beat at medium speed until the mixture becomes light and fluffy, 3–5 minutes.
Incorporate the vanilla extract and salt; continue beating for 1 minute more.
Gradually add the flour in batches, mixing on low speed until just combined.
Using a spatula, fold in the chopped cranberries and orange zest.
Split the dough into two equal portions. Roll each portion into a log approximately 7 inches long and 2 inches in diameter. Individually wrap each log in plastic wrap.
Chill the logs in the refrigerator for at least 1 hour, or overnight.
Set the oven to 325°F (165°C). Prepare a baking sheet by lining it with parchment paper and set aside.
Unwrap the chilled dough and cut into rounds about ⅓ inch thick.
Arrange the slices on the prepared baking sheet and bake for 10–12 minutes, until the edges are just barely golden.
Allow the cookies to cool on the baking sheet for 30 minutes, then move them to a wire rack to cool completely.
Serve right away or keep in an airtight container.
