Unroll both tubes of crescent dough and separate into triangles. Place triangles on a greased 12-inch pizza pan, forming a ring with pointed ends facing toward the center and wide ends overlapping. Lightly press wide ends together.
In a small bowl, beat cream cheese, confectioners' sugar and vanilla until smooth; spoon over wide ends of ring. In another bowl, stir the brown sugar, butter and cinnamon until crumbly. Sprinkle over cream mixture.
Fold points over filling and fold wide ends over points. Bake at 350 degrees for 20–25 minutes or until golden brown. Cool for 5 minutes.
Meanwhile, combine the confectioners' sugar, vanilla and enough milk to achieve desired consistency. Divide icing among three bowls. Using red and blue food coloring, tint one portion purple. Tint another portion yellow and the remaining portion green. Drizzle over cake. Serve warm.