Place the chocolate chips in a large, microwave-safe bowl. Microwave the chocolate for one minute at 50% power. Stir. If necessary, continue heating in 30-second increments until chocolate is nearly melted (residual heat will melt any remaining chocolate solids).
Slowly whisk in the half-and-half until smooth. Add the cocoa powder, sugar and pinch of salt and stir until smooth. Slowly whisk in the milk.
Pour the chocolate mixture into the base of a blender. Add the ice and a pinch of xanthan gum, if using. Process until smooth. Pour into four to six individual glasses and top with whipped cream and chocolate shavings.
Note: I used my Vita-mix, which has a very large base/container. If you have a blender with a somewhat small base/blender container you may have to process the frozen hot chocolate in two batches.