Soak the poppy seeds: In a small bowl, combine poppy seeds and buttermilk. Stir and let sit while you prepare the rest of the batter.
Preheat oven: Preheat to 375°F (190°C). Line a 12-cup muffin tin with paper liners.
Zest and rub: In a large bowl, combine sugar and lemon zest. Rub together with your fingertips until the sugar is pale yellow and intensely fragrant, about 1 minute.
Cream butter and sugar: Add softened butter to the lemon sugar. Beat with a whisk or electric mixer until pale and fluffy, about 3 minutes.
Add eggs: Beat in eggs one at a time, scraping down the bowl after each addition.
Combine dry ingredients: In a separate bowl, whisk together flour, baking powder, baking soda, and salt.
Alternate wet and dry: Add half the flour mixture to the butter mixture and fold gently. Add the buttermilk-poppy seed mixture and fold. Add the remaining flour and fold just until the last streak of flour disappears. Do not overmix.
Fill liners: Divide batter evenly among the prepared muffin cups, filling each about 2/3 full. A cookie scoop works best for even muffins.
Bake: Bake for 18–20 minutes until the tops are golden and a toothpick inserted in the center comes out clean. Let cool in the tin for exactly 5 minutes, then transfer to a wire rack to cool completely.
Optional glaze: Whisk 1 cup powdered sugar with 2 tablespoons fresh lemon juice until smooth. Drizzle over cooled muffins.