Whisk together flour, cocoa powder, baking soda, and salt in a bowl.
In another bowl, beat butter, shortening, and sugars with an electric mixer until fluffy. Then beat in egg and vanilla. At low speed, mix in flour until dough just comes together, then mix in toffee.
Shape dough into an 8 inch log (3 inches in diameter) on a floured surface with floured hands, then flatten ends and chill, wrapped in plastic wrap, at least 6 hours.
TOPPING AND BAKING
Preheat oven to 350°F. with rack in center of oven. Line 2 large baking sheets with parchment paper.
Finely grind graham crackers (I just stick them in a plastic baggies and crush them with a mallet.) You should have about ¼ cup. Then stir together crumbs, marshmallows and condensed milk (the mixture will be very sticky.)
Cut dough crosswise into 10 (¾-inch-thick) slices. Place 3 to 4 slices on each baking sheet (cookies will spread about 5 inches during baking.)
Bake cookies for about 5 to 6 minutes (until they begin to spread). Open oven and carefully spoon on a heaping tablespoon of topping in the center of each cookie. Close the oven door and continue baking for another 12 to 15 minutes, until topping is golden and cookies are baked through.
Slide cookies with parchment onto racks to cool completely. Bake remaining cookies in the same manner on freshly lined baking sheets.