Step 1Heat the oven to 275 degrees. Mix together the garlic, ginger, sake, brown sugar and soy sauce in a large, nonreactive, oven-proof pot or casserole. Add the pork and just enough water to cover the pork completely. Cover the pot with 2 layers of foil (and the casserole lid, if using) and cook for 2 to 3 hours, until the pork is fork-tender.
Step 2Remove the pork from the braising liquid and place in a nonreactive dish. Cover with plastic wrap and refrigerate overnight.
Step 3Cut the pork belly into lardons (1 inch-by- 1/2 inch-by- 1/2 inch). Place them in a large, heavy-bottom saute pan and cook over medium-high heat, stirring frequently until their edges slightly crisp and the fat is mostly rendered, about 10 minutes. Strain and discard the fat. Set aside the meat; you will have about 4 cups, more than is needed for the sandwiches in the final recipe. If not using immediately, cover and refrigerate; reheat before using. The meat will keep for 5 days refrigerated.
Step 1Combine the chipotle puree and mayonnaise in a small bowl. Adjust the seasoning to taste with salt and pepper, cover with plastic wrap and refrigerate until needed. (This makes about 1 cup aioli, more than enough for the sandwiches.)
Step 1Place the julienned daikon and carrots in separate, nonreactive bowls. Sprinkle 1 tablespoon salt over each and gently mix into the vegetables. Allow each to sit for 30 minutes.
Step 2Rinse the daikon and carrots separately under cold running water until the water runs clear. Shake vigorously to remove the excess water.
Step 3Combine the daikon and carrots in a medium nonreactive bowl and stir in the rice vinegar and sugar. Taste and adjust the sweetness with additional sugar as desired. Cover and refrigerate until needed; drain the pickled vegetables before using. This makes about 2 cups pickled daikon and carrots.
Step 1Spread each ciabatta half with 1 tablespoon of the aioli. Divide the pork belly among the 4 bottom ciabatta halves (one-third cup per sandwich), then top with the pickled vegetables. Sprinkle evenly with the cucumber, and repeat with the cilantro. Place 2 to 3 jalapeno slices on each half, or more to taste. Cover each sandwich with the remaining ciabatta bread.
Step 2Grill the sandwiches using a panini press or on a grill over medium heat and weighted with something heavy (like a cast-iron skillet). Cut each sandwich in half and serve immediately.