Preheat oven to 350°F (175°C). Line a 12-cup muffin tin with paper liners.
In a medium bowl, whisk together the flour, poppy seeds, baking powder, baking soda, and salt. Set aside.
In a large bowl, beat softened butter and sugar until light and fluffy. Add eggs one at a time, mixing well after each addition. Stir in lemon zest, lemon juice, and vanilla extract.
Gradually add the dry ingredients to the wet mixture, alternating with buttermilk. Mix gently until just combined. Do not overmix.
Fill each muffin cup about three-quarters full. Bake for 18–22 minutes, or until a toothpick inserted comes out clean.
Allow muffins to cool for 5 minutes in the pan, then transfer to a wire rack to cool completely. If desired, drizzle with lemon glaze once cooled.