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

In a large mixing bowl, whisk together the flour, sugar, baking powder, and salt until well combined.

In another bowl, beat the softened butter until creamy. Add the milk, eggs, lemon zest, lemon juice, poppy seeds, and vanilla extract. Mix until smooth.

Gradually add the dry ingredients to the wet ingredients, stirring until just combined. Be careful not to overmix.

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

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

For the glaze, whisk together the powdered sugar and lemon juice in a small bowl until smooth. Drizzle the glaze over the cooled cake.