Combine the milk, cooled coffee (if using), sugar, vanilla extract, vanilla bean seeds, and xanthan gum in a high-speed blender.
Add the ice cubes to the blender last.
Secure the lid and blend on high speed until the mixture is completely smooth and has a uniform, icy texture. You may need to stop and scrape down the sides once.
Taste the mixture; add a little more sugar or vanilla if needed, then blend briefly to combine.
Pour the blended mixture into a tall glass.
Top with homemade or store-bought whipped cream, if desired.
Notes
For a thicker drink without coffee, increase the ice to 2 cups and use slightly less milk.
If you do not have xanthan gum, you can substitute with 1 tablespoon of cream cheese or 1/2 teaspoon of instant pudding mix for texture, though the texture may vary.
To make vanilla whipped cream, whip 1/2 cup heavy cream with 1 tablespoon powdered sugar and 1/2 teaspoon vanilla extract until stiff peaks form.
If you only have vanilla extract and no bean or paste, use 1 1/2 teaspoons of vanilla extract total.