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.
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.
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.