Cut the pork into 2 1/2" squares.
Put the pork belly, fat side down, in a small heavy bottomed pot (such as a dutch oven) that's just large enough to hold the pork in a single layer. Put the pot over medium high heat and let the pork fry undisturbed until it's golden brown on the fat side.
Flip each piece over and brown the other side, then transfer to a plate.
Add the ginger, garlic, and niboshi and and fry until browned and fragrant.
Add the sake and boil until you no longer smell alcohol.
Add the water, sugar, soy sauce, salt, and return the pork to the pot. Bring to a simmer and then turn down the heat and cover with a tight fitting lid.
Simmer until the pork belly is fall-apart-tender (about 2 hours).
Strain the braising liquid and if you are going to serve the kakuni right away, skim off the extra fat. It's best if you let this sit in the fridge overnight though as this gives the meat a chance to absorb more flavor, and it will make removing the excess fat a lot easier.
To serve, gently reheat the pork belly. Slice and serve with some of the braising liquid, hot mustard and steamed greens.