Add the graham crackers and milk to a medium bowl and stir them together. Cover the bowl and place it back in the fridge to let the cookies soak for about 30 mins to 1 hour. The graham crackers should mostly dissolve, but you can blend the mixture in a blender, or push it through a fine mesh strainer to remove bigger pieces.
Add the graham cracker and milk mixture to a large bowl, add in the heavy cream, brown sugar, vanilla extract, and salt and stir it together for a couple minutes to help the sugar dissolve.
Pour the mixture into a prepared 2QT ice cream maker and let it run for about 25 minutes, according to the manufactures directions, until it's almost like a soft serve ice cream.
While the ice cream is churning crush the graham crackers in a blender into a fine crumb. Then mix the graham crackers, in a small bowl with the sugar and butter.
Add the honey comb candy pieces and mini chocolate chips and let them churn into the ice cream the last 5 minutes until mixed evenly into the ice cream.
Scoop about ¼ to ⅓ of the ice cream into a 2QT pan (a 9x5 bread pan works great for this). Then sprinkle ⅓ of the graham cracker crumble over the top. Repeat with more ice cream, more crumble, more ice cream and the final crumble.
Cover the container with a lid, or with plastic wrap and foil and place in the freezer to freeze for at least 6 hours until frozen solid, into a scoopable ice cream.
