Start by roughly chopping the fresh cranberries in a food processor until they're coarsely minced. Set them aside.

In a stand mixer, combine the granulated sugar and orange zest. Rub them together for about 1-2 minutes until fragrant.

Add the room-temperature unsalted butter to the sugar mixture and beat until light and fluffy, about 3-5 minutes. Mix in the egg yolk until fully incorporated.

Gradually add the all-purpose flour into the butter mixture, mixing on low speed until the dough starts to clump together. Gently fold in the chopped cranberries.

Lightly flour your work surface and turn the dough out, dividing it into two equal portions. Shape each portion into a log and refrigerate for at least 1 hour.

Preheat the oven to 325°F (163°C). Prepare a baking sheet with parchment paper or a silicone mat.

Once the dough is chilled, unwrap the logs, brush with a beaten egg white, and sprinkle with demerara sugar. Slice the logs into rounds about ¼ inch thick.

Place the sliced cookies on the prepared baking sheet, spacing them about 1 inch apart. Bake for 15-18 minutes or until lightly golden.

Allow the cookies to cool on a wire rack for a few minutes before enjoying.