Preheat your oven to 350°F (175°C) and line a muffin tin with cupcake liners.
In a mixing bowl, whisk together the flour, baking powder, baking soda, salt, and poppy seeds.
In another bowl, beat the butter and sugar until light and fluffy. Add the eggs one at a time, beating well after each addition. Mix in the vanilla extract and lemon zest.
Gradually add the dry ingredients to the wet ingredients, alternating with the buttermilk. Mix until just combined.
Divide the batter evenly among the cupcake liners, filling each about two-thirds full.
Bake for 18-20 minutes, or until a toothpick inserted into the center comes out clean. Let the cupcakes cool in the tin for 5 minutes, then transfer to a wire rack to cool completely.
To make the glaze, whisk together the powdered sugar and lemon juice until smooth. Drizzle over the cooled cupcakes.