In a large bowl with a hand mixer or in a stand mixer bowl with a paddle attachment, mix on low speed to cream butter and confectioners' sugar.

In a medium bowl, whisk together the flour, rosemary, and salt. Gradually add the flour mixture to the butter mixture just until combined. The dough will be very crumbly.

Transfer the dough to a lightly floured surface. Using your hands, roll and shape the dough into an 8-inch log. Securely wrap in plastic wrap and refrigerate for at least 2 hours and up to overnight.

Preheat the oven to 350°F. Line a baking sheet with parchment paper.

Place chilled cookie dough on a flat work surface and slice into 1/2-inch rounds. Arrange cookie dough slices onto the prepared baking sheet at least 2 inches apart.

Bake for 11 minutes, until the edges are golden brown. Cool for 1 minute on the baking sheet, then transfer to a wire cooling rack to cool completely. Serve at room temperature.