In a small sauce pot, over medium heat, combine raspberries, corn starch and Sweet 'N Low. Mash the berries, stir, cover and cook for 5-7 minutes. You can use an immersion blender to mix the berries, or mash with spatula as much as possible.
Strain sauce through a fine strainer to get rid of the seeds. Use a spoon and keep stirring the sauce in the strainer, helping it go through since it will be a little think. Discard the seeds and set aside the syrup.
In a small sauce pot, over medium heat, heat up milk and add white chocolate chips and vanilla extract. Stir slowly as it cooks until all the chips are melted and combined.
Divide hot chocolate among the cups, top off with whipped cream and raspberry sauce. You can also sink some sauce to the bottom of the cup.