Preheat your oven to 350°F (175°C). Line a baking sheet with parchment paper.
In a mixing bowl, cream together the softened butter, granulated sugar, and powdered sugar until light and fluffy, about 2-3 minutes.
Add the vanilla extract and orange zest to the butter mixture and mix until well incorporated.
In a separate bowl, combine the all-purpose flour and salt. Gradually add the dry mixture to the creamed mixture, mixing on low until just combined.
Carefully fold in the chopped dried cranberries using a rubber spatula until evenly distributed.
Divide the dough in half and shape each half into a log, about 1.5 inches in diameter. Wrap each log in plastic wrap and refrigerate for at least 30 minutes.
Once chilled, remove the dough from the refrigerator. Unwrap the logs and slice into 1/4-inch thick rounds.
Place the cookie rounds on the prepared baking sheet, leaving about 1 inch between each.
Bake in the preheated oven for 15-20 minutes, or until the edges are slightly golden.
Remove from the oven and let cool on the baking sheet for 5 minutes before transferring to a cooling rack to cool completely.