Preheat the oven to 350°F (180°C). Line a 9×5-inch (23×13 cm) loaf pan with parchment paper and set aside.
In a large mixing bowl, add the sugar and lemon zest. Rub them together with your fingers or a spatula to release the lemon's natural oils. Add the softened butter and beat with a hand mixer or a stand mixer fitted with a whisk attachment until pale and fluffy. Add the eggs one at a time, mixing well after each addition.
Add the baking powder, salt, and about 1 cup of flour. Mix at low speed until just combined. Pour in the milk and lemon juice, and mix until incorporated. Add the remaining flour and the poppy seeds. Mix until just combined—do not overmix.
Transfer the batter to the prepared loaf pan and bake for 50–55 minutes, or until a toothpick inserted in the center comes out clean. Start checking a few minutes before the recommended time, as baking times may vary.
Remove the cake from the oven and let it cool for about 10 minutes in the pan. Then, transfer to a serving plate and cool completely.
To make the glaze, add the powdered sugar to a small bowl and mix in 1 teaspoon of lemon juice. Stir, then add more lemon juice as needed until the glaze is thick but pourable. Drizzle the glaze over the cooled cake with a spoon. Let it harden before serving. Slice, serve, and enjoy!
