Preheat the oven to 375 degrees. Grease a 12-cup muffin tin.
Grate the skin from the lemon (lemon zest) and squeeze the lemon, straining the seeds and saving the juice.
In a medium mixing bowl, combine the ½ cup sugar with the grated lemon zest. Use your fingers or a pastry blender to rub the zest into the sugar. Whisk in the flour, poppy seeds, baking powder and baking soda.
In a separate bowl, whisk together the butter, yogurt, eggs, lemon juice and vanilla.
Add the liquid ingredients to the dry ingredients, using a large spoon to stir until the flour mixture is fully incorporated.
Divide the batter evenly between the muffin cups. Sprinkle the tops with the coarse sugar. Bake until a toothpick comes out clean, about 15 – 18 minutes. Let muffins cool in the pan for 5 minutes, then transfer to a rack to cool completely.