In a large microwave safe bowl, add chocolate chips. Microwave in 20-30 second increments, stirring in between, until melted and smooth.
While whisking, slowly pour in half and half. Stir in the cocoa powder, sugar, and salt. Continue to whisk as you pour in the milk.
Pour the mixture into blender. Add ice and blend until smooth. Stir in finely crushed graham crackers.
Divide the chocolate among serving glasses. Top with crushed graham crackers, graham cracker pieces, chocolate shavings, and marshmallows. Serve immediately.