Preheat oven to 350. Line a baking sheet with parchment paper and set aside.
Combine the dry ingredients in a large bowl. Whisk to combine.
In the bowl of stand mixer, beat the butter and brown sugar for 2 minutes. Add honey and beat 1 minute more. Add the dry ingredients and mix on low until the mixture is dry and crumbly. Add the peppermint extract and coffee and mix until the dough clumps together. Form dough into a disk, wrap in plastic wrap and freeze for 20 minutes.
Roll the chilled dough out between two pieces of parchment paper to an 1/8" thick. Cut into 6 rectangles and transfer to the prepared baking sheet. You may need to re-roll the dough once or twice to get 6 rectangles. To make them look like real graham crackers, cut an indentation in the middle of each rectangle and make 2-3 indentations with a fork on each square. Place the baking sheet in the freezer and chill for 10 minutes. This will keep them from spreading. Bake 15-20 minutes, until the dough is set in the center and dry around the edges. Let cool completely on the pan.
Melt the chocolate and coconut oil in a microwave safe bowl until smooth. Stir every 30 seconds to prevent it from burning. If it does not seem thin enough to dip, add a little bit more coconut oil to thin it out. Just be careful not to add too much or it won't set up. To assemble the s'mores, gently break each graham cracker along the indentation so that you have 2 squares. Spread a spoonful of melted chocolate on the bottom side of one square. Place the marshmallow on top, pressing gently to adhere it. Top with the second graham cracker. Dip the s'more halfway in the melted chocolate then dip the chocolate portion in the crushed candy canes. Place finished s'mores on a parchment lined baking sheet and let sit until the chocolate hardens. This can be sped up by sticking the pan in the fridge or freezer.