In a bowl, whisk together flour, rosemary and salt. In a stand mixer, beat butter and sugar on medium speed until well blended. Reduce speed to low and slowly add in flour mixture; blend until the mixture resembles coarse crumbs. Gather dough into two balls, wrap both tightly in plastic wrap and refrigerate for 30 minutes.
Heat oven to 350°. Remove one dough ball and roll out to 1/4-inch thickness on parchment paper. Punch out cookies using a 31/2-inch tree-shaped cookie cutter. Transfer cutouts to a cookie sheet about 2 inches apart; refrigerate for 15 minutes. Repeat with second dough ball. Bake at 350° for 10 to 12 minutes. (Do not allow cookies to brown.) Transfer cookies to a cooling rack.