Preheat your oven to 350°F (175°C) and grease a bundt pan.
In a bowl, whisk together flour, baking powder, baking soda, and salt.
In a separate bowl, cream the softened butter and sugar until light and fluffy.
Add the eggs one at a time, mixing well after each addition.
Stir in vanilla extract, lemon zest, and lemon juice.
Gradually add the dry ingredients to the wet mixture, mixing until just combined.
Fold in the poppy seeds gently.
Pour the batter into the prepared bundt pan.
Bake in the preheated oven for 30-35 minutes, or until a toothpick comes out clean.
Let the cake cool for 10 minutes in the pan, then invert onto a wire rack to cool completely.
Mix powdered sugar with lemon juice and drizzle over the cooled cake.