Preheat oven to 400°F. Line 12 standard-size muffin cups with paper liners; set aside.
In a large bowl, whisk together flour, poppy seeds, baking powder, baking soda and salt.
In a separate bowl, whisk together melted butter, granulated sugar, brown sugar, lemon zest and vanilla extract. Add eggs, whisk to combine. Add sour cream, whisk until smooth.
Add the wet ingredients to the dry ingredients. Using a wooden spoon or spatula, combine just until incorporated – do not over-mix.
Divide batter evenly among the prepared muffin cups, filling each cup almost to the top.
Bake for 5 minutes at 400°F. Without opening the oven, lower the temperature to 375°F and bake for 11-14 more minutes, or until a toothpick inserted in the center of a muffin comes out clean. Cool in the pan for a few minutes, then transfer muffins to a wire rack to cool completely.
Once the muffins are cool, prepare the glaze by whisking together the confectioners’ sugar and lemon juice (or milk). You want the glaze to be thick, but pourable. If it’s too thin, add more confectioners’ sugar. If it’s too thick, add a tiny bit more juice or milk, just until it reaches the desired consistency.
Drizzle over the muffins.