Filling: In a small saucepan, combine sugar, egg, lemon zest, lemon juice and butter. Cook over medium heat, stirring constantly for about 10 minutes or until mixture begins to thicken. Set aside to cool.
Cookies: In a mixing bowl, combine butter, sugar, lemon zest and lemon juice, beating until combined.
Using a 1 tsp. measure, roll dough into balls.
Place on parchment lined baking sheets and flatten slightly.
Bake at 400 degrees for 6-8 minutes. Cool.
Spread half of cookies with filling. Top with remaining cookies. Roll in powdered sugar.