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Preheat oven to 350 degrees F. Grease 12 standard muffin cups with butter or nonstick cooking spray or line with paper liners.
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For the muffins: In a small bowl add granulated sugar and lemon zest. Stir to infuse the lemon zest into the sugar and set aside while preparing the other ingredients.
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In a large mixing bowl, using a whisk, whisk the eggs. Add the lemon infused sugar and whisk to combine. Add the butter, lemon juice and sour cream (or yogurt) and whisk until smooth and creamy.
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In a medium bowl combine the flour, baking powder, baking soda and salt.
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Add the dry ingredients to the wet ingredients in the large mixing bowl. With a spatula stir to combine just until the flour is all absorbed. Fold in the poppy seeds and gently stir until they are incorporated into the batter. Batter will be thick.
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Fill prepared muffin cups almost level with the rims. Bake for 18 – 20 minutes. Let cool for 5 minutes then un-mold the muffins to a rack fitted over a parchment paper lined baking sheet to cool completely.
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For the Icing: In a small bowl mix the icing sugar and lemon juice until smooth. Drizzle layers of icing over the muffins allowing the excess to dribble down the sides of the muffins. Sprinkle the top of each muffin with a touch of lemon zest.