In a small bowl, combine espresso powder, sugar, cocoa powder, salt and pepper. Pat the short ribs dry with a paper towel and evenly coat them with the dry rub.
Heat the oil in a large Dutch oven over medium heat, and sear the short ribs on each side, about 5 minutes. Remove from the pan and set aside. To the pan, add the onion, carrot and celery and cook for 4 minutes. Add in the beef broth and bay leaf, and return the short ribs to the pan. Bring to a boil, cover and transfer the pan to the oven to cook for 2 1/2 to 3 hours. Once tender, remove from the oven and shred the beef using two forks. Set aside to cool.
In the bowl of a stand mixer fitted with the dough hook, dissolve yeast in warm water and let sit for 10 minutes until foamy. Add evaporated milk, oil, sugar, 1 egg and 2 cups of self-rising flour. Mix until smooth. Mix in the remaining flour and knead to form a soft dough. Transfer the dough to a lightly greased bowl, cover with plastic wrap and proof on the counter for 2 hours. (This step can be done while the short ribs are in the oven.)
Heat a large pot of vegetable oil to 350 degrees.
Once the dough has proofed, punch down to flatten. Transfer to a floured surface and roll the dough out into a large rectangle. Cut the dough into 24 2-inch squares. Using a pastry brush, moisten the edges of each rectangle with the remaining egg, and place a tablespoon of short rib filling in the center of 12 of the squares. Top with the remaining squares, and gently press down the edges to create a seal.
Carefully add beignets to the hot oil and cook, flipping constantly, until puffed and golden brown. Transfer to a paper towel-lined plate to drain. Sprinkle with chopped parsley and serve.