Pulse the cocoa nibs in a spice grinder until the nibs are coarsely chopped, 3 to 4 pulses. Place the nibs in a 1-quart microwave-safe measuring cup and add 16 ounces of milk. Microwave on high for 3 to 4 minutes or until the milk reaches 160ºF. Steep at room temperature for 30 minutes.
Meanwhile, combine the chocolate, sugar, water, and salt in the carafe of a 1-liter French press. Set aside.
After steeping, return the nib-milk mixture to the microwave and heat on high for 2 minutes until it simmers or reaches 185ºF. Strain the hot nib-milk mixture through a fine-mesh strainer into the French press carafe. Set aside for 1 minute, and then stir to combine the chocolate and milk. Pump the plunger of the French press 10 to 15 times to froth and aerate. Pour the mixture into a standard ice cube tray and freeze until solid, at least 3 hours or up to overnight.
Combine the frozen hot chocolate cubes with 4 ounces of milk, half-and-half, or coffee in a blender and blend until smooth. Serve immediately.