Combine flour, cocoa powder, 1 tbsp sugar, and salt in a large bowl.
Chill 1 1/2 sticks butter in the freezer for a few minutes until cold and hard. Grate half into the bowl of flour and work gently with your hands. Place the rest back in the freezer.
Once your flour mixture is crumbly and sandy, remove the rest of the butter from the freezer and slice into thin squares. Add to your flour mixture.
Work gently into the dough for a few seconds. Add coffee, a few tablespoons at a time, until the butter and flour begin to clump.
Remove big clumps onto your work surface and continue to lightly combine the rest of the dry ingredients with remaining butter, adding coffee as needed.
Once you have a cohesive mass of shaggy dough, press into a large square and wrap in plastic wrap. Chill for at least 30 minutes.
Roll dough out into a large rectangle, about 18” x 24”. Fold the dough like a letter, in thirds, with the left flap on top of the dough.
Turn 90 degrees and roll again into an 18” x 24” rectangle. This time, sprinkle 1 tbsp sugar over the top and press into the dough with your rolling pin.
Perform another letter fold and wrap your dough again. Chill in the fridge at least 30 minutes, until ready to use.
Preheat oven to 375°F. Remove dough from fridge and roll into a large rectangle again.
In a small bowl, combine 2 tbsp soft butter, 1 tbsp cocoa powder, 1 tbsp white sugar, and 1 tsp ground cinnamon.
Spread mixture over the entire top of the dough. Then roll half the dough into a log from the long end until it reaches the middle of the dough.
Roll the other half of the dough into a log, meeting the first log in the middle of the dough. Flip the dough over and chill for 5-10 minutes in the freezer.
Line a large baking sheet with parchment paper. Remove dough from the fridge and slice into cookies (about 3/4” thick each).
Place palmiers on baking sheet, spaced 1-2” apart, and bake for 15-20 minutes until lightly browned.