Preheat the oven to 325°F. Line baking sheets with parchment paper or lightly grease them.

In a medium bowl, beat the softened butter at medium speed with an electric mixer until creamy.

Gradually add the sifted powdered sugar to the butter, beating until well combined.

Reduce mixer speed to low and gradually add the all-purpose flour, mixing just until blended.

Gently stir in the chopped fresh rosemary until evenly distributed.

Use your hands to press and gather the dough into a smooth ball. If the dough is too soft to roll, chill it in the refrigerator for 10–15 minutes.

Lightly flour a work surface and a rolling pin. Roll the dough to a 1/4-inch thickness.

Cut the dough with a 2-inch cookie cutter. Transfer the cut cookies to the prepared baking sheets, spacing them about 1 inch apart.

Bake for 16 to 18 minutes, or until the edges are lightly browned.

Let the cookies cool on the baking sheet for a few minutes, then transfer them to wire racks to cool completely.