In a medium bowl, use a wooden spoon to mix together melted butter, cake mix, egg and vanilla.
Shape the dough into a log about 12 inches in length and wrap in wax paper.
Refrigerate for two hours.
Preheat oven to 350 degrees F.
Slice cookies about ¼ inch thick and bake for 10 – 12 minutes.
Cool on a wire wrack.
Melt the white chocolate and mix with oil until smooth.
Use a spoon or filled pastry bag to drizzle the chocolate over the cookies.
Allow chocolate to set before serving.