Prepare the loaf pan. Preheat an oven to 350°F (180°C). Line a 9x4-inch loaf pan with parchment paper, ensuring there's enough hanging over the sides to help you lift and remove the cake after baking.
Mix the dry ingredients. In a mixing bowl, whisk together 200g (1⅔ cups) flour, 1 tsp baking powder, ¼ tsp baking soda, and ½ tsp Kosher salt.
Cream the butter and sugar. In the bowl of a stand mixer, combine 1 cup (200g) sugar and 2 tsp lemon zest, then rub together with your fingers to release the oils in the zest. Add ½ cup (113g) unsalted butter, then beat until pale and fluffy, about 3 minutes.
Add the eggs. Add 3 large eggs one at a time, scraping down the sides of the bowl with a rubber spatula as needed in between.
Mix the wet ingredients. In a separate mixing bowl, whisk together ¼ cup (60g) fresh lemon juice, ¼ cup (60g) milk, 3 Tbsp poppy seeds, and 1 tsp vanilla extract.
Finish the cake batter. With the mixer on low, alternate adding ⅓ of the 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.
Bake the loaf cake. Transfer the cake batter into the prepared loaf pan (it will be thick!), smooth the top with a spatula, then bake for 50-55 minutes, or until the cake is puffed up, golden brown, and a toothpick inserted into the center of the cake comes out clean.
Cool the cake in the loaf pan for 10 minutes, then transfer to a wire rack to cool completely.
Add the lemon glaze. Whisk 1⅔ cups (200g) powdered sugar, ¼ cup (60g) lemon juice, and 2 tsp milk together. Pour over the loaf (it will drip down the sides!), then immediately sprinkle with additional 1 tsp poppy seeds if wanted. Cut into slices, then enjoy!