Add the milk, vanilla syrup (or sugar and vanilla bean paste), ice cubes, and xanthan gum to a high-powered blender.
Blend on high speed for 30-45 seconds until completely smooth and thick, with no ice chunks remaining.
Pour the heavy cream into the blender and pulse 2-3 times just to incorporate, being careful not to over-blend.
Pour into a large glass and top generously with whipped cream.
Garnish with vanilla bean caviar or a small amount of vanilla bean paste on top of the whipped cream and serve immediately with a straw.