I work as a barista on the side, and our shops use sauces for hot chocolates and mochas. Most use Monin dark chocolate sauce, which we lightly dilute with hot water before topping off with steamed milk. One of our cafes uses a drinking chocolate mix from Ritual Chocolate, which is prepared into a sauce in batches and is then served the same way.
At home, I grind chocolate bars on a Microplane, add a light pinch of salt and a little bit of sugar (depending on the bar at hand), then melt in the cup with a little hot water and top up with steamed milk. The amount of chocolate I actually use depends somewhat on the bar itself, but I'd guess it's around 1 oz of chocolate per 8 fl oz final beverage. Darker chocolates will seize with hot water, so sometimes you need to use hot cream or melted butter instead to make the sauce. This makes a drink that falls between a typical hot chocolate and something like a drinking chocolate; it's rich but not so much so that you can't enjoy a big mug of it.