Preheat the oven to 350°F (175°C). Grease and flour a 9-inch round or loaf pan or line it with parchment paper for easy removal.
Cream the butter and sugar together in a large mixing bowl using a hand mixer or stand mixer until light and fluffy, about 3-4 minutes.
Add the eggs one at a time, mixing well after each addition. Scrape down the sides of the bowl to ensure even mixing.
In a separate bowl, whisk the flour, baking powder, and salt. Gradually add the dry ingredients to the wet mixture in thirds, alternating with the milk, beginning and ending with the dry ingredients. Mix just until combined.
Add the lemon zest, lemon juice, and vanilla extract to the batter. Mix gently to incorporate.
Pour the batter into the prepared pan, smoothing the top with a spatula. Bake for 50-60 minutes, or until a toothpick inserted into the center comes out clean.
Cool in the pan for 10 minutes before transferring to a wire rack to cool completely.
Optional: Dust the cooled cake with powdered sugar, or drizzle with a simple lemon glaze for extra flavor.
