Add the milk, heavy cream, vanilla syrup, white chocolate chips, and sugar (if using) to a saucepan over medium heat on the stove. Stir and cook until the chips are melted and well combined.
Let the white chocolate mixture cool a bit.
If making a hot drink, pour the warm white chocolate mixture evenly into two cups, and pour the espresso on top. Top with whipped cream if desired.
If making a cold drink, add the ice to the two cups, before pouring in the white chocolate mixture. Pour in the espresso, and top with whipped cream if you like.