Heat oven to 450°F. Bake and cool crust as directed on box for One-Crust Baked shell.
In large microwavable bowl, place milk chocolate chips, dark chocolate chips and 1/2 cup of the whipping cream. Microwave uncovered on High 30 seconds; stir. Repeat until chocolate chips are stirred smooth.
Place remaining 1 1/2 cups cream and the chocolate mixture in large bowl. Beat with electric mixer on high speed until thick. Spread in cooled pie shell. Refrigerate 2 hours.
Just before serving, set oven control to broil. Cover pie filling with large and miniature marshmallows. Drizzle with sweetened condensed milk. Broil with top about 5 inches from heat leaving oven door open slightly and watching so it does not burn. Remove pie as soon as marshmallows are golden brown. Serve immediately.