Special equipment: a mandolin with a julienne blade and a 4-inch piece cheesecloth and butcher twine
For the pork belly: Set a rack in the middle of the oven and preheat it to 325 degrees F.
In a small Dutch oven, heat the olive oil over medium-high heat. Add the carrots, celery, onion, 1/2 teaspoon salt and 1/2 teaspoon pepper and cook until lightly browned and just tender, 8 to 10 minutes. Add the garlic and cook until just softened, 2 to 4 minutes. Tie the thyme and rosemary sprigs together with kitchen twine and add to the vegetable mixture along with the bay leaves, chicken stock and beer. Stir to combine, and then nestle the pork belly into the Dutch oven. The pork belly should be submerged in the liquid. Cover with a lid and bake in the oven until the pork is tender, but not falling apart, 1 to 1 1/2 hours.
Cool completely in the liquid at room temperature and then chill in the refrigerator overnight.
The next day, remove the pork belly from the liquid and slice in to 1/4-inch pieces, about 16 slices total. Whisk together the whole-grain mustard, honey and red pepper flakes. Season to taste with salt and pepper.
Heat a large skillet over medium heat and, in batches, cook the pork belly slices until the fat melts and starts to crisp, brushing with the honey mustard glaze during the last few seconds of cooking.
For the pulled pork: Wrap the parsley, coriander, thyme and bay leaf in a small piece of cheesecloth and tie it together with butcher twine. Reserve.
Mix together the chili powder, paprika, cumin, 1/2 teaspoon salt and 1/2 teaspoon black pepper in a small bowl. Rub the spice mixture onto the pork tenderloin and set aside.
Heat a stockpot over medium-high heat and add the olive oil and onion. Cook until translucent, about 2 minutes. Add the garlic and jalapeno and cook until fragrant, about 1 minute. Add the chicken stock, orange juice, lime juice and liquid smoke.
Put the spiced pork tenderloin into the pot and add enough water to cover the chicken (this might take up to 1 1/2 cups). Add the herbs and spices in the cheesecloth and cook, covered, on medium heat until the pork tenderloin is just cooked through, 15 to 20 minutes. Remove the pork tenderloin from the pot and allow to cool slightly.
Discard the cheesecloth bundle. Strain the liquid in the pot and reserve the strained ingredients in a bowl. Take the strained liquid and place it back into the pot and simmer until reduced by three-quarters.
When the pork has cooled enough to work with, use your hands to shred the pork into long strands. Mix the shredded meat with the strained ingredients in a bowl. Add the reduced liquid to the bowl and mix it with the shredded pork.
For the chicken schnitzel: Set a rack in the middle of the oven and preheat it to 400 degrees F.
Cut each chicken thigh in half lengthwise. Reserve.
Stir together the rice flour and black pepper in a shallow baking dish. Lightly whisk the egg whites and place into a second baking dish. Put the crushed cornflakes into a third baking dish. Dredge each chicken thigh in the seasoned flour, dip it into the egg whites and then roll in the crushed cornflakes. Place onto a cooling rack set over a baking sheet and bake until the chicken is cooked through, 15 to 20 minutes.
For the jicama slaw: Use a mandolin set with the thin julienne blade to cut the jicama, cucumber and mango into thin matchsticks. There should be about 2 cups of each after they are cut. Reserve.
Whisk together the pepperoncini, pickling liquid, rice vinegar, jalapeno, lime juice, cilantro, oil, ancho chili powder, chipotle chili powder and 2 teaspoons salt in a large bowl. Add the jicama, cucumber and mango to the dressing and stir to combine.
For the cilantro-avocado yogurt aioli: Put the avocado, yogurt, lime juice, cilantro and a large pinch of salt into a blender and blend until smooth. With the blender running, slowly add the avocado and canola oil and blend until smooth and creamy. Add up to 1/4 cup of water if you would like a thinner aioli
For the BBQ mustard sauce: Stir together the yellow mustard, apple cider vinegar, light brown sugar, butter, Worcestershire sauce, hot sauce, 1 teaspoon salt and 1/2 teaspoon black pepper in a small saucepan set over medium heat. Bring to a simmer and cook for 10 minutes. Add the BBQ mustard to the pulled pork mixture. Toss to combine.
To make the sandwiches: Place one-eighth of the pulled pork on the bottom of a toasted potato bun. Place 1 piece of schnitzel on top of the pork. Add 1 piece of butter lettuce, 2 pieces of pork belly, 1 tomato slice and one-eighth of the slaw. Smear a spoonful of the avocado aioli onto the cut side of the top of the potato bun then place on top of the slaw. Serve immediately.