Combine the milk, heavy cream, sugar, vanilla bean paste, and vanilla extract in a small saucepan. Heat over medium heat, stirring until the sugar dissolves completely. Do not boil. Remove from heat and let the mixture cool completely in the refrigerator.
Once chilled, pour the cooled liquid mixture into a high-speed blender.
Add the ice cubes and the xanthan gum, if you are using it for extra thickness.
Blend on high speed until the mixture is completely smooth and has a thick, icy consistency. You may need to stop and scrape down the sides.
Pour the blended mixture into a tall glass.
Top generously with whipped cream before serving immediately.
Notes
For a thicker result without xanthan gum, increase the heavy cream slightly or use frozen milk cubes instead of some of the ice.
If you do not have vanilla bean paste, use 1/2 teaspoon of high-quality vanilla extract, but the visual specks will be missing.
Adjust the sugar amount based on your preference for sweetness.