How to Make It
Preheat broiler to high.
Place marshmallows in a single layer on a baking sheet lined with parchment coated with cooking spray. Broil 30 seconds or until golden brown and toasted. Cool.
Combine half-and-half and granulated sugar in a saucepan over medium-high heat; bring to a simmer, stirring occasionally. Place yolks in a medium bowl; stir with a whisk until smooth. Gradually add hot half-and-half mixture to egg yolks, stirring constantly with a whisk. Return egg mixture to pan; cook over medium heat 6 minutes or until mixture thickens slightly and reaches 160°, stirring constantly. Strain through a fine sieve into a large bowl set over a larger ice water-filled bowl. Let stand until cold, stirring occasionally. Place half-and-half mixture, marshmallows, and vanilla in a blender; process until smooth. Chill mixture 3 hours or overnight.
Pour marshmallow mixture into the freezer can of an ice-cream freezer; freeze according to manufacturer's instructions. Line an 11 x 7-inch freezer-safe dish with plastic wrap, allowing wrap to extend over ends of dish; spread ice cream in bottom of dish. Freeze 3 hours or until firm.
Combine milk, shortening, and syrup in a saucepan over low heat; cook 1 minute or until shortening melts, stirring constantly. Stir in powdered sugar and cocoa; cook over medium heat 1 minute or until smooth, stirring with a whisk.
Remove ice cream from pan using extended plastic wrap to lift; discard plastic wrap. Cut ice cream into 8 squares. Place 1 square on 1 graham cracker half; top with other half of cracker. Drizzle chocolate mixture evenly over sandwiches.