Mix the salt and sugar together in a small bowl and coat the pork belly evenly with the mixture. Cover and refrigerate for 24 hours.
Preheat the oven to 350 degrees F. Cook the pork belly in a baking pan, uncovered, until firm, 1 hour 20 minutes to 1 hour 30 minutes. Let rest for 20 minutes.
Mix the mayonnaise and capers together in a food processor. In a separate bowl, dress the arugula with the red wine vinegar.
Slice the pork belly in half, lengthwise. Then slice it crosswise into 1/2-inch slices, which should resemble very thick and short slices of bacon. Heat a saute pan over medium heat and add 2 to 3 slices of belly per batch. Cook until crisp on both sides, about 2 minutes per side.
In a separate nonstick pan, fry the eggs over-easy, so the yolks are still soft.
Spread some caper mayo on each bottom bun, followed by some belly, an egg and some arugula. Press the top buns down so the yolks pop, and serve.
This recipe was provided by a chef, restaurant or culinary professional. It has not been tested for home use.