In a mixing bowl, whisk together flour, baking powder, baking soda, and Kosher salt.
In the bowl of a stand mixer, combine sugar and lemon zest, then rub together with your fingers to release the oils in the zest. Add unsalted butter, then beat until pale and fluffy.
In a separate mixing bowl, whisk together fresh lemon juice, milk, poppy seeds, and vanilla extract.
With the mixer on low, alternate adding flour mixture, then half of the milk mixture, then repeat, ending finally with the flour mixture. Be careful not to overmix, the ingredients should just barely be incorporated.
Pour the cake batter into the prepared loaf pan, then bake until the cake is puffed up, golden brown, and a toothpick inserted into the center of the cake comes out clean.
Whisk powdered sugar, lemon juice, and milk together. Pour over the loaf, then immediately sprinkle with additional poppy seeds if wanted. Cut into slices, then enjoy!