For the braised pork: Preheat the oven to 250 degrees F.
In large high-sided roasting pan combine the pork, apple cider, salt, peppercorns, paprika, chile flakes, coriander, cumin, garlic, celery, thyme, bay leaves, carrots, onions, tomatoes and chipotles. Cover with parchment paper, and then cover with aluminum foil, insuring a tight seal. Braise in the oven until fork tender, 6 hours.
Cool the pork to room temperature. Store the pork in the braising liquid overnight in the fridge. Remove from the liquid and wrap. Can be used for up to 7 days.
For the tomatoes: Preheat the oven to 350 degrees F. Line a baking sheet with parchment paper.
Place the tomatoes, olive oil, salt, pepper, garlic and thyme in a bowl, and toss to coat evenly. Roast the tomatoes on the prepared baking sheet for 20 minutes.
For the aioli: In a food processor, process the eggs and garlic until smooth, 1 minute. Slowly add the oil in a steady stream. Add the lemon juice, then add half of the roasted tomatoes, and pulse until smooth. Add the remaining tomatoes, and pulse until smooth. Season with the salt.
To assemble, preheat the oven to 450 degrees F. Line a baking sheet with parchment paper.
Cut the pork belly in half lengthwise. Slice each half into lardons, 1/4-inch pieces. Cook the belly in the oven on the prepared baking sheet until crispy, 10 minutes. Slice the rolls in half, and toast. Spread the aioli on the bottom half of the bun, place two pieces of pork belly on top, the place some romaine on the belly, top with the top half of the bun. Repeat for the remaining buns and pork belly. Serve immediately.
Consumption of raw or undercooked eggs, shellfish and meat may increase the risk of foodborne illness.