Combine 1/2 cup plus 1 tablespoon butter, white sugar, vanilla sugar, and egg in a bowl. Beat with an electric mixer until light and fluffy.

Mix flour and baking powder together. Beat into the butter mixture on low speed until dough becomes crumbly. Work dough crumbles with your hands into a smooth dough and place into a sealable container. Refrigerate until chilled, 1 to 2 hours.

Preheat the oven to 350 degrees F (175 degrees C). Line 2 baking sheets with parchment paper.

Roll the dough out to 1/4-inch thickness on a lightly floured surface and cut into desired shapes using cookie cutters. Place cookies 1 inch apart on the prepared baking sheets.

Pick up all the left over dough, press together into a ball, and repeat the rolling and cutting out process until all the dough is used up.

Bake in the preheated oven until edges are lightly browned, 8 to 10 minutes. Allow cookies to cool on the baking sheets for 5 minutes before carefully removing to a wire rack with a knife or thin spatula to cool completely.

Mix confectioners' sugar and lemon juice until glaze has a smooth and spreadable consistency. Add more lemon juice if you like a thinner glaze. Add food coloring if you like. Brush frosting on cooled cookies and add chocolate sprinkles or sugar sprinkles if desired.