Center a rack in the oven and preheat the oven to 400 degrees.
Butter or spray the 12 molds in a regular-size muffin pan or fit the molds with paper muffin cups.
In a large bowl, rub the sugar and the lemon zest together with your fingertips until the sugar is moist and the fragrance of the lemon is strong.
Whisk in the flour, baking powder, baking soda and salt.
In a small bowl, whisk the sour cream, eggs, vanilla, lemon juice and melted butter together until well blended.
Pour the liquid ingredients over the dry ingredients and gently stir to blend.
Don't overmix.
Stir in the poppy seeds.
Divide the batter evenly among the muffin cups.
Bake for 18 to 20 minutes, or until the tops are golden and a thin knife inserted into the center of the muffins comes out clean.
Transfer the pan to a rack and cool for 5 minutes before carefully removing each muffin from its mold.
Cool the muffins completely on the rack before icing them.