Prepare the oven and pan. Preheat the oven to 425°F (220°C). Line a standard 12-cup muffin pan with paper liners.
Combine the dry ingredients. In a medium bowl, whisk together the flour, baking powder, baking soda, salt, and poppy seeds.
Make the lemon sugar. In a large bowl, rub the granulated sugar and lemon zest together with your fingertips until fragrant and slightly damp.
Add the wet ingredients. Add the Greek yogurt, milk, melted and slightly cooled butter, eggs, lemon juice, and vanilla extract to the lemon sugar. Whisk until well combined.
Combine the mixtures. Add the dry ingredients to the wet ingredients. Gently fold with a spatula just until no dry flour remains. Avoid overmixing.
Fill and bake. Divide the batter evenly among the 12 muffin liners. Bake for 15–17 minutes, or until the tops are golden and a toothpick inserted into the center comes out clean or with a few moist crumbs.
Cool. Let the muffins rest in the pan for about 5 minutes, then transfer them to a wire rack to cool completely.
Prepare the glaze. Stir the powdered sugar and lemon juice together in a small bowl until smooth and free of lumps. If needed, adjust with a little more powdered sugar to thicken or a few drops of lemon juice to thin.
Glaze and serve. Drizzle the glaze over the cooled muffins. Let it set before serving or storing.