Mix 1⅓ cups unbleached, all-purpose flour, ½ teaspoon baking powder, and ½ teaspoon salt in a separate bowl. Set aside.
In a large mixing bowl, whip ¼ cup butter until smooth. Add 1 cup sugar and continue beating until the mixture is fluffy. Add 1 large egg and keep mixing until smooth.
Add grated rind of 1 small lemon, 1½ tablespoons lemon juice, and ¾ cup Greek yogurt to the above mixture.
Stir in dry ingredients. Make sure no stray pockets of butter are unmixed with the flour in the bowl.
Cover and chill the dough for at least 30 minutes before baking.
Spoon a generous tablespoon for each cookie onto a cookie sheet covered with parchment paper.
Bake at 375˚F (190˚C)for 12-15 minutes (depending on whether it is the first batch or the last and the size of the cookies) until the edges begin to brown.
Glaze
Make the icing while the cookies bake. Sift 1 cup powdered sugar into a small bowl. Add grated rind of 1 lemon, 1 tablespoon of heavy cream, and 1-2 tablespoons lemon juice. Combine until smooth. Add another tablespoon of lemon juice if the icing is too thick.
When the cookies are brown on the bottom but not on top, remove them from the oven. After 10 minutes, pull the cookies away from the paper and allow to continue cooling on a rack or tea towel. Smoothly coat the top with lemon frosting. Let the frosting cool and set before handling them. Eat whenever you can't resist any longer.