Preheat your oven to 375°F (190°C). Line a 12-cup muffin tin with paper liners or grease thoroughly with butter or non-stick spray.
In a medium bowl, whisk together the flour, baking powder, baking soda, and salt.
Before juicing your lemons, zest them first using a microplane grater, being careful to only grate the yellow part.
In a large mixing bowl, beat the softened butter and sugar until light and fluffy, about 2-3 minutes.
Add eggs one at a time, beating well after each addition. Mix in the lemon zest, lemon juice, and vanilla extract.
Gently fold in half the dry ingredients, then the yogurt, then the remaining dry ingredients. Stop mixing as soon as no dry streaks remain.
Fill each muffin cup about ¾ full (around 3 tablespoons of batter). Bake for 18-20 minutes or until a toothpick inserted comes out clean and tops are lightly golden.
Allow muffins to cool in the pan for 5 minutes before transferring to a wire rack.
While the muffins cool, whisk together powdered sugar, lemon juice, and zest until smooth. Adjust consistency by adding more sugar (thicker) or juice (thinner) as needed.
Once muffins are slightly cool but still warm, drizzle or spoon the glaze over the tops, allowing it to run down the sides slightly.