Adjust oven rack to middle position and heat oven to 180 degrees C. Grease 12-cup muffin tin.
Whisk flour, sugar, poppy seeds, baking powder, baking soda, and salt together in a large bowl.
In a separate bowl, whisk yogurt, lemon zest, and eggs until smooth. Gently fold yogurt mixture into flour mixture until just combined. Fold in melted butter. Do not overmix. If you overmix, the muffins will be dense.
Divide batter evenly among prepared muffin cups. Bake until golden brown and toothpick inserted in the center comes out clean, 20 to 25 minutes. Rotate muffin tin halfway through baking.
While muffins are baking, simmer sugar and lemon juice together in a small saucepan over medium heat until it turns into a light syrup, about 3-5 minutes.
Remove muffin tin to a wire rack. Brush with lemon syrup. Sprinkle with coarse sugar. Let muffins cool in tin for 5 minutes, then transfer to a wire rack and let cool for another 10 minutes before serving.