Preheat your oven to 375°F (190°C) and line a 12-cup muffin tin with paper liners. Lightly spray the top of the pan with cooking spray, as these muffins rise a lot and can stick.
Melt the butter and set it aside to cool. While it cools, zest and juice your lemons. You’ll need about 2 large lemons for both the muffins and the glaze.
In a large bowl, whisk together flour, sugar, poppy seeds, baking powder, baking soda, and salt. Break up any sugar clumps with your fingers to prevent dense spots in your muffins.
In a separate bowl, whisk together the melted (cooled) butter, milk, eggs, lemon zest, lemon juice, and vanilla until smooth. It may look curdled, but that’s normal because of the lemon juice.
Pour the wet ingredients into the dry ingredients. Using a rubber spatula, fold everything together until you no longer see any dry flour streaks. The batter will be thick and lumpy—this is good. Stop mixing to avoid tough muffins.
Divide the batter among the muffin cups, filling them about ¾ full. I use an ice cream scoop to keep portions even.
Bake for 18-22 minutes, or until the tops are golden brown and spring back when gently pressed. A toothpick inserted in the center should come out clean or with a few moist crumbs.
Cool the muffins in the pan for 5 minutes, then transfer them to a wire rack to cool completely.
For the glaze, mix powdered sugar and lemon juice in a small bowl. Start with 2 tablespoons of lemon juice and add more until the glaze is thick but drips slowly off the spoon.
Once the muffins are completely cool, drizzle the glaze over them. Place parchment paper under the wire rack to catch any drips. Let the glaze set for about 15 minutes before serving.