Preheat the oven to 425°F. Line a 12-cup muffin pan with paper liners.
In a large bowl, whisk together the flour, baking powder, and baking soda. Whisk in poppy seeds and salt.
In another large bowl, combine the sugar and lemon zest. Working with your hands, rub zest into sugar until well combined and the sugar feels damp. Add the yogurt, milk, melted butter, eggs, lemon juice, and vanilla. Whisk until smooth.
Pour the wet ingredients into the flour mixture and fold just until combined. (The batter will be thick.) Divide the batter evenly among the paper liners.
Bake for 15 to 17 minutes or until the tops are golden brown and a toothpick inserted in the center comes out with a few moist crumbs. Let the muffins cool in the pan for 10 minutes. Remove the muffins and finish cooling on a wire rack.
In a small bowl, whisk together powdered sugar and lemon juice until smooth. Drizzle over cooled muffins.
