Preheat oven to 325 degrees F (165 degrees C). Grease and lightly flour a 9x5-inch loaf pan.
Whisk flour, baking powder, and baking soda together in a bowl.
Beat butter in a bowl using an electric mixer until smooth and creamy, about 30 seconds. Gradually beat sugar into butter until light and fluffy; add vanilla extract and beat until incorporated. Beat eggs, 1 at a time, into creamed butter mixture, beating about 1 minute after each addition.
Beat flour mixture, alternating with sour cream, into creamed butter mixture with the electric mixer on low until batter is just combined. Stir orange zest and rosemary into batter; pour into the prepared loaf pan.
Bake in the preheated oven until a toothpick inserted into the center comes out clean, 60 to 70 minutes. Cool in the pan for 10 minutes before removing to cool completely on a wire rack.