Preheat the oven to 425 degrees. Make sure your oven rack is in the middle position, then prepare your muffin pans by spraying them generously with non-stick spray, or by adding paper liners.
In a small bowl, mix together the room temperature greek yogurt and lemon juice.
Place the sugar in a small bowl and add the lemon zest to it. Rub this mixture together, between your fingers, to allow the lemon oils to really work into the sugar.
Cream together the room temperature butter and the lemon sugar.
Mix in the room temperature eggs, one at a time. Add the yogurt and lemon juice mixture to this bowl and combine this well.
In a separate large bowl, whisk together the flour, poppy seeds, baking powder, and salt. Make a well (hole) in the center of this dry mixture.
Pour the wet mixture (butter, yogurt, etc) into the well you made in the dry ingredients. Stir until the mixture is moist. Do not over-mix, or the muffins will be tough. Batter may be clumpy, and that is okay.
Divide the batter equally among the 12 muffin cups. Smooth out the tops of the batter if desired. At this point, you can bake right away, or let the muffins sit on the counter for about 20 minutes before placing them in the oven. They rise slightly higher when left to sit for those 20 minutes, but it's optional. They will still be great without it.
Bake at 425 degrees for 5 minutes. Then, turn the oven down to 350 and continue baking for another 12-15 minutes. Start checking for doneness (toothpick comes out clean or with just a few tiny crumbs) at about the 18 minute mark.
While the muffins are cooling, make the glaze by whisking together the powdered sugar, milk and lemon juice. You may adjust the amount of lemon juice depending on how thin you’d like the glaze to be.
Allow the muffins to cool for at least 10 minutes before removing them from the pan and glazing them. When cool, use a fork to drizzle the glaze back and forth across the tops of the muffins.