In the bowl of a stand mixer fitted with a paddle attachment, or in a large bowl with a hand-held mixer, beat the butter, sugar and brown sugar together until light and creamy, about 3-4 minutes. Add the eggs, mixing after each. Mix in the vanilla.

In a separate bowl combine the flour, graham cracker crumbs, baking soda and salt. Add to the wet ingredients and mix until just combined. Add the chopped chocolate bars and mix until just incorporated.

Shape into rounded tablespoons and place on prepared sheet pan a few inches apart. Bake until edges just begin to turn golden, about 9-10 minutes. Do not overbake or cookies will become crispy. Let cool on the pan for 5 minutes, then transfer to a wire rack to cool completely.

Use a kitchen torch, gas burner or campfire to toast the marshmallows. Avoid using an oven broiler as that melts the marshmallow and creates a big mess.

In a food processor or heavy duty blender, blend the marshmallows with the softened vanilla ice cream. Pour mixture back into a medium bowl or plastic container and freeze until hard, at least 2 hours.

Place sandwiches in the freezer to firm up for about 20 minutes before serving.

If making ahead, wrap each ice cream sandwich in plastic wrap. This will keep them from getting freezer burned.