Preheat the oven to 400°F (200°C). Line a 12-cup muffin pan with liners or lightly grease each cup. In a medium bowl, whisk together the flour, poppy seeds, baking powder, baking soda, and salt. Set aside. In a large bowl, rub the lemon zest into the sugar using your fingers until the sugar smells fresh and looks slightly moist. Add the eggs to the lemon sugar and whisk until smooth. Mix in the Greek yogurt, vegetable oil, lemon juice, and vanilla extract until fully combined.
Add the dry ingredients to the wet mixture in batches, alternating with the milk. Start and end with the dry ingredients.
Gently stir just until combined. Do not overmix.
Spoon the batter evenly into the muffin cups, filling each about two-thirds full.
Bake for 18–20 minutes, or until a toothpick inserted into the center comes out clean. Let the muffins cool in the pan for 5 minutes, then transfer them to a wire rack to cool completely. In a small bowl, whisk together the powdered sugar and 2 tablespoons of lemon juice until smooth. Add more lemon juice if needed to reach your preferred glaze consistency.
Drizzle the glaze over the cooled muffins using a spoon.