Preheat oven to 375 degrees F. Line a standard 12-well muffin pan with paper liners. Set aside.

Cut the butter into 4 pieces and place in a microwave-safe bowl. Microwave for 30 seconds. Butter should be almost fully melted. Stop microwaving and set aside at room temperature for at least 5 minutes.

Finely zest the 2 lemons into a large bowl. Add sugar into the same bowl and whisk until the sugar and lemon zest are well combined. Juice the zested lemons in the bowl and add melted butter, milk, Greek yogurt, eggs, and vanilla. Whisk to combine.

Combine flour, baking powder, baking soda, salt, and poppy seeds in a separate bowl. Stir to combine. Add the dry ingredients into the wet ingredients and use a wooden spoon or rubber spatula to mix the batter.

Divide the batter evenly among the prepared muffin wells (about 1/4 to 1/3 cup per muffin well).

Place into the oven and bake until the muffins are lightly golden and a toothpick inserted into the center of a muffin comes out clean, about 20 minutes. While the muffins are baking, mix the ingredients for the glaze in a small bowl. Remove the muffins once they are done. Let cool 10 minutes before glazing. Using a spoon, drizzle the glaze on the tops of the muffins. Serve warm.