Mix the sugar, peanut butter, butter, milk and vanilla sugar together until creamy. Mix in the egg well. Mix the flour, baking soda and salt and sift over it. Work in well.
Place the dough on a prepared tray with a little space between the spoons. Press the grid into the surface with a fork. Bake the cookies for about 7-8 minutes, until the edges start to turn light brown. Let rest on the baking sheet for 2 minutes, then transfer to a wire rack to cool down.