Amerikaner cookies

It is not entirely known why these cookies are called Amerikaner (Americans). They are apparently known in the US as black-and-white cookies, and are a NYC specialty. One explanation for their German name is that the term black-and-white cookies is already taken for a different type of cookie, so these new ones were just called by the name of the people who introduced these delicious treats to us.
The NYC version of these cookies glazes one half with white icing, the other half with chocolate, hence the name. the traditional German cookie is glazed with white icing only. In addition to being great cookies going well with coffee or tea, they can be a great addition to a kid's birthday party, and kids can have fun decorating these cookies as they like.

Ingredients:
75 g soft butter
100 g sugar
1 package vanilla sugar or some vanilla aroma
1 pinch of salt
1 egg
375 g wheat flour
3 teaspoons of baking powder
250 ml milk

For brushing: about 2 tablespoons milk

For the icing:
200 g confectioners' sugar
3 tablespoons lemon juice or water
150 g dark chocolate
1 tablespoon coconut or other cooking oil
Optional: chopped almonds, chopped pistachios, grated coconut, sprinkles, M&Ms

1. Line a baking sheet with parchment paper. Preheat oven to 180 degrees Celsius (350F).
2. Whisk butter in a bowl with a hand-mixer until soft. Add sugar, vanilla sugar or aroma, and salt and stir until dough is smooth and even. Add egg, and stir in for 1/2 minute at highest setting.
3. Mix flour and baking powder in a separate bowl. Alternate adding the flour mix and the milk and whisk until smooth.
4. Using a tablespoon put little heaps on the parchment paper. Make sure to leave enough space between cookies as they tend to become bigger. The original size uses two large tablespoon per cookie, but I like them smaller, so I use one tablespoon.
5. Bake for about 20 min. After 15 min in the oven, brush the surface with a little milk. This keeps the cookies moist, and facilitates the browning. When done remove cookies from oven and let cool.
6. For the icing, sift the confectioners' sugar and mix with water or lemon juice. The glaze should be rather syrupy, not liquid. Melt the chocolate (I use a microwave and heat for 20s at a time stirring after each heating step until melted). Add coconut or cooking oil. Coat the flat side (underside during baking) with icing and/or chocolate. Decorate with nuts, coconut flakes, sprinkles or M&Ms while the icing or chocolate is still soft.

Variation: The sponge dough can be flavored. Here are two suggestions I've tried. If you use icing with lemon juice, you can add some lemon aroma to the sponge for a stronger lemony taste. Alternatively, peppermint aroma works well. In this case you should add some peppermint aroma and water instead of lemon juice to the confectioners' sugar for the icing. I've also added a drop of red food coloring to the icing turning the icing pinkish, but truly, use your phantasy and play around with aromas and icing.