Preheat the oven to 350°F (175°C). Line a 9x5-inch loaf pan with parchment paper.

In a mixing bowl, cream together the unsalted butter and sugar until fluffy and light.

Add eggs, lemon zest, and lemon juice to the mixture, mix until just combined.

In another bowl, whisk together flour, baking powder, and salt, then gently fold into the wet ingredients.

Slowly mix in the milk until the batter is smooth and creamy.

Pour the batter into the prepared loaf pan and bake for 40-45 minutes.

Cool in the pan for 30 minutes, then transfer to a wire rack to cool completely.

For the icing, whisk together powdered sugar, lemon juice, and lemon zest until thick but pourable.

Drizzle the icing over the cooled cake, allowing it to set between layers.