Preheat your oven to 190°C (375°F) and line a muffin tin with paper liners. Zest both lemons, being careful to avoid the bitter white pith, then squeeze out about 1/4 cup of fresh lemon juice. Set aside.
In a small dry skillet over medium heat, toast the poppy seeds until fragrant and slightly golden, about 2 minutes. Remove from heat and set aside.
In a large mixing bowl, whisk together the flour, sugar, baking powder, salt, and toasted poppy seeds until well combined and slightly aerated.
In a separate bowl, whisk the eggs until they are slightly frothy, then add the Greek yogurt, melted butter, lemon zest, lemon juice, and vanilla extract. Whisk until smooth and well combined.
Pour the wet mixture into the bowl with the dry ingredients. Gently fold together with a spatula until just combined — be careful not to overmix, as this keeps the muffins tender.
Divide the batter evenly among the paper-lined muffin cups, filling each about three-quarters full. The batter should be slightly lumpy but well distributed.
Bake in the preheated oven for 20-22 minutes, or until the muffins are golden on top, smell bright and citrusy, and a toothpick inserted into the center comes out clean.
Remove the muffins from the oven and let them cool in the tin for about 5 minutes. Then transfer them to a wire rack and cool completely for about 10 minutes.
Once cooled, sprinkle with additional poppy seeds or powdered sugar if desired, and serve slightly warm or at room temperature for a bright, flavorful bite.