Melt butter. Break dried chile in half, remove the top inch of the chile by the stem and set aside. Add the coffee to the butter. Steep dried chile and cinnamon stick in butter for one hour.
Remove stem from remaining chile. Grind chile finely.
Sift flour, cocoa, baking powder, ground cinnamon, ground chile, and salt into medium bowl.
Remove chiles and cinnamon stick from the butter. Combine butter, sugar, vanilla, and one whole egg and one egg yolk in a large bowl and stir with a wooden spoon.
Add flour mixture to bowl with the butter mixture and stir until well combined.
Pre-heat oven to 350. Put dough in the refrigerator for fifteen minutes.
Line baking sheet with silpat or parchment paper. Turn dough on to baking sheet (it will be sticky and if you have to scoop it out that's fine). Form dough into one log that is about 3-4 inches wide and almost as long as the cookie sheet.
Brush egg white over the dough. Sprinkle with sea salt.
Bake for 25 minutes. Remove and let cool for 10-15 minutes. Once it is cool enough to handle cut the log into 1/2 inch cookies. Set cookies on cut side and return to oven for 12 minutes. Remove from oven and flip the cookies over and bake for another 12 minutes.