Fill a large bowl with ice water. In another large bowl, whisk the cream cheese until smooth.
In a large saucepan, combine the brewed coffee, almond milk, heavy cream, VitaFiber powder, stevia extract powder, and VitaFiber syrup. Bring the milk mixture to a boil and cook over moderate heat about 4 minutes. Stir in xanthan gum, coffee extract or powder, and vanilla.
Gradually whisk the hot milk mixture into the cream cheese until smooth. Whisk in the salt. Set the bowl in the ice water bath and let stand, stirring occasionally, until cold, about 20 minutes.
Pour mixture into an ice cream maker and freeze according to the manufacturer's instructions. Pack the ice cream into a plastic container.
Press a sheet of plastic wrap directly onto the surface of the ice cream and close with an airtight lid. Freeze the ice cream until firm, about 4 hours.