Preheat the oven to 150ÂșC and grease two round 23cm cake pans. Sprinkle with flour and/or line with baking paper.
Cream together the butter, sugar and vanilla until light and fluffy, about 3 minutes.
Add the flour, 1 cup at a time, mixing just until combined. Divide the dough evenly between the two greased pans and press it into an even layer. Using a fork, prick the dough all over.
Bake for 35 minutes, or until the shortbread is pale golden in the centre and slightly darker around the edges.
Remove the shortbread from the oven and immediately invert the pans onto a cutting board. Using a sharp knife, immediately cut each shortbread round into 8 wedges. It is important to cut the shortbread while it's still warm, or it will crumble if you try to cut it after it has cooled. Transfer the shortbread wedges to a cooling rack to cool completely.
Melt the chocolate in a microwave or double-boiler, stirring until smooth. Transfer to a piping bag or plastic bag, snip off the tip of the bag and drizzle it onto the cookies in tinsel-like lines. Immediately top the cookies with sprinkles. Serve once the chocolate has set.