Preheat your oven to 350°F (175°C). Grease and flour a 9x5-inch loaf pan.

In a medium bowl, whisk together the flour, baking powder, baking soda, and salt. Set aside.

In a large bowl, cream the softened butter and sugar together until light and fluffy, about 3-5 minutes.

Add the eggs one at a time, mixing well after each addition. Stir in the lemon zest and vanilla extract.

Gradually add the dry ingredients to the wet mixture, alternating with the buttermilk. Start and end with the dry ingredients, mixing until just combined.

Pour the batter into the prepared loaf pan and smooth the top. Bake for 50-60 minutes, or until a toothpick inserted in the center comes out clean.

While the cake is baking, prepare the syrup. In a small saucepan, combine the sugar, lemon juice, and chopped rosemary. Bring to a boil over medium heat, stirring until the sugar dissolves. Remove from heat and let cool slightly.

Once the cake is done, remove it from the oven and let it cool in the pan for 10 minutes. Then, transfer it to a wire rack.

While the cake is still warm, poke holes in the top with a toothpick and pour the syrup over the cake, allowing it to soak in.

Let the cake cool completely before slicing.