For each milkshake, spread 2 tsp. of the frosting in a 1-inch-wide band around rim of each of three 6-oz. serving glasses. Sprinkle with 0.25 oz. of the OREO pieces. Drizzle 1 tsp. of the chocolate sauce up and down inside of glass.
Blend vanilla ice cream, milk, CHIPS AHOY! pieces and remaining 1 oz. OREO pieces in blender until smooth. Pour into prepared glasses.
Top each glass with 1 scoop cookies-and-cream ice cream to one side. Pipe whipped cream on other side of scoop. Garnish each with 1 each of the whole cookies and remaining chocolate sauce.