Preheat the oven to 300°F.
Place the pork belly, skin-side up, in a braising pan or other oven-safe vessel.
Combine the orange juice and zest, lime juice and zest, soy sauce, mirin, rice vinegar, water, ginger, garlic, and roughly chopped shallot. Pour the mixture around the pork belly.
The braising liquid should come approximately one-half to three-quarters of the way up the sides of the pork belly rather than completely covering it.
Cover tightly and braise for approximately 3 1/2hours, or until the pork belly is tender.
Remove from the oven and allow it to cool slightly.
Place a sheet of parchment directly over the pork belly, top with another sheet pan or flat pan, and place a heavy weight on top. Refrigerate overnight.
Pressing the pork belly as it chills compacts the layers of meat and fat and creates a firm, uniform piece that can be cut cleanly for the finished appetizer.
Strain the braising liquid into a separate container and refrigerate overnight.