For the pork: Preheat the oven to 375 degrees F. Pull the pork loin out of the refrigerator 30 minutes before cooking.
In a small bowl, mix together the cocoa powder, coffee, salt, paprika and cinnamon. Season the pork well with the mixture, rubbing it in on all sides.
Heat a large skillet over medium heat. Add the oil and heat an additional 30 seconds. Add the pork and sear on all sides until deep golden brown, about 6 minutes. Remove the pork to a rimmed baking sheet, transfer to the oven and cook until the internal temperature reaches 135 degrees F on an instant-read thermometer, about 40 minutes. Allow to rest for 15 minutes.
For the benedict: Meanwhile, add the bacon to the skillet that the pork was cooked in and cook over medium heat until the bacon is crispy and the fat is rendered, about 4 minutes. Whisk in the flour until smooth and cook for a minute. Slowly add the coffee and chicken broth, whisking constantly so that no lumps form. Bring to a simmer and cook for 5 minutes. Whisk in the salt and 2 tablespoons of the butter to emulsify. Remove from the heat and keep warm.
Heat a medium nonstick skillet over medium heat. Add 1 tablespoon butter and swirl to coat the bottom of the skillet. Break 2 eggs into the skillet and cook until the whites are just set, about 4 minutes. To assist in setting the whites, spoon some of the melted butter over the whites, avoiding the yolk so it stays runny. Remove to a baking sheet lined with parchment paper and continue with the remaining butter and eggs.
To assemble, place 1/4 cup arugula on each English muffin half. Thinly slice the pork and place 1 to 2 pieces on each muffin half. Spoon some of the gravy over the pork and top each muffin half with a fried egg. Serve warm.
To make sure the eggs are warm for serving, place the baking sheet with all the eggs in a the oven at 250 degrees F for 2 to 3 minutes. Continue with the assembly.