Preheat the oven to 375 degrees Fahrenheit and lightly grease small tart pans with butter.

In the bowl of a food processor, combine flour, cocoa powder, sugar, and salt. Pulse a few times to combine. Scatter the pieces of butter over the dry ingredients and pulse until the butter is coarsely cut in. Some pieces of dough will be the size of oatmeal flakes, while some will be the size of peas.

Add egg yolk to a small measuring cup with a pourable spout, and stir to break it up. Add egg a little at a time, pulsing after each addition. Once egg is in, process in long pulses, about 10 seconds each, until the dough, which will look granular to begin with, forms clumps and curds. Just before you reach this stage, the sound of the machine will change, so be ready.

Turn the dough out onto a work surface, and very lightly and sparingly knead the dough just to incorporate the dry ingredients. Press the dough into the tart pans and chill for 30 minutes to one hour before baking.

Bake tart dough 10 to 20 minutes, until dough is firm and crisp. Remove tarts from the oven and decrease temperature to 350 degrees Fahrenheit.

Place chocolate in a medium bowl and set aside.

Combine sugar, coffee, and butter in a small saucepan and bring to a boil. Pour over chocolate and leave undisturbed, two to three minutes. Whisk until smooth, then add the eggs, one a time, stirring well after each addition.

Divide filling evenly among the tart shells. Bake 10 minutes. Allow to cool completely.