Line baking sheet with parchment paper and set aside.
In a large bowl, mix butter, sugar, vanilla and flour together until incorporated. Dough should hold its shape when squeezed together. Divide dough into 4 equal portions and form into logs down the length of the cookie sheet. Press your finger into the center to create an indent all down each log. Bake 12-15 minutes. Cool completely.
Fill each log with jam.
Mix all ingredients together for the icing until its the constancy of white school glue. Drizzle over each log generously. Cut into diagonal pieces once icing has set for 20 minutes or so.