In a mixing bowl, combine the sifted powdered sugar and fresh orange zest. Use your fingertips to rub the zest into the sugar for 1 to 2 minutes until intensely fragrant and tinted pale orange.

In a stand mixer fitted with the paddle attachment, beat the softened European butter and orange-infused powdered sugar on medium speed for 2 minutes until creamy and smooth (do not whip fluffy). Stir in vanilla extract, almond extract, and fine sea salt.

Reduce mixer speed to low. Gradually add the all-purpose flour in two batches, mixing just until the flour is incorporated and a soft dough forms. Fold in the finely chopped dried cranberries until evenly distributed.

Divide the dough in half. Turn each half out onto a sheet of parchment paper or plastic wrap and shape into an even cylinder log approximately 2 inches in diameter and 8 inches long.

Wrap tightly in parchment paper, twisting ends to seal. To preserve a round shape without a flat bottom, slide the wrapped logs inside an empty paper towel tube (or rotate every 30 minutes). Chill in the refrigerator for at least 2 hours, or up to 3 days.

Preheat your oven to 350°F (175°C) and line two large rimmed baking sheets with parchment paper.

Unwrap chilled dough logs. Lightly brush all sides with beaten egg white. Spread coarse sparkling turbinado sugar on a flat baking dish and roll the logs firmly until evenly coated in sparkling crystals.

Using a very sharp chef knife, slice the logs into 1/3-inch thick rounds. If the dough crumbles slightly, simply press it back together with your fingers. Place cookies 1.5 inches apart on prepared baking sheets.

Bake for 12 to 14 minutes, rotating pans halfway through, until the edges are just barely light golden and the tops are set (do not overbake; shortbread should stay pale). Cool on baking sheet for 10 minutes, then transfer to a wire cooling rack to cool completely.