Preheat your oven to 350°F (175°C). Grease and flour a 9x5-inch loaf pan or line it with parchment paper.
In a medium bowl, whisk together the flour, poppy seeds, baking powder, baking soda, and salt. Set aside.
In a large mixing bowl, cream the softened butter and granulated sugar together until light and fluffy, about 3-5 minutes.
Add the eggs one at a time, mixing well after each addition. Stir in the lemon zest, lemon juice, and vanilla extract.
Gradually add the dry ingredients to the wet mixture, alternating with the buttermilk. Begin and end with the dry ingredients, mixing until just combined.
Pour the batter into the prepared loaf pan and smooth the top. 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 about 10 minutes before transferring it to a wire rack to cool completely.
For the glaze, whisk together the powdered sugar and lemon juice until smooth. Drizzle over the cooled cake.