Line a 9-inch square baking dish with parchment paper. Set aside.
In a large mixing bowl, add chocolate chips and marshmallow cream and set aside.
In a large saucepan, combine sugar, butter, and heavy cream over medium-high heat and stir constantly until mixture begins to boil. Watch carefully and keep at a rolling boil for 4-5 minutes, stirring constantly.
Remove mixture from heat and slowly stir Irish cream into the hot cream mixture. Pour this hot mixture over the chocolate chips and marshmallow cream in the mixing bowl.
Using an electric mixer, beat the mixture until the chocolate is completely melted and the mixture is creamy, about 1-2 minutes. Pour into prepared pan and refrigerate for 4 hours.
Once the fudge has chilled, melt the white chocolate chips in the microwave or in a double boiler. Drizzle the white chocolate over the fudge (it helps to do it off a spoon). Evenly spread sprinkles over the top and chill for 1 hour. Remove the fudge by lifting the parchment paper out of the pan, then cut into 1-inch or 2-inch pieces.