Preheat your oven to 350°F (175°C). Grease and line an 8x4 inch loaf pan with parchment paper.
In a large mixing bowl, cream together the softened butter and granulated sugar until light and fluffy, about 3-4 minutes. This step incorporates air into the batter, contributing to a lighter texture.
Add the eggs one at a time, beating well after each addition. Mix in the lemon zest and juice until well combined.
In a separate bowl, whisk together the flour, baking powder, and salt. Gradually add this dry mixture to the wet ingredients, alternating with the milk. Begin and end with the dry ingredients to prevent overmixing, which can lead to a dense cake.
Pour the batter into the prepared loaf pan and smooth the top. Bake for 35-40 minutes, or until a toothpick inserted into the center comes out clean.
While the cake is baking, prepare the lemon glaze by whisking together the powdered sugar and lemon juice until smooth.
Once the cake is done, let it cool in the pan for 10 minutes, then transfer to a wire rack. While still warm, poke holes all over the top with a skewer and drizzle the glaze over the cake, allowing it to soak in.
Let the cake cool completely before slicing and serving.