For the roast pork: In a food processor, combine the oil, vinegar, wine, chipotles, cilantro, cumin, oregano, salt, agave, pepper, cayenne and garlic. Pulse to the consistency of a smooth, loose paste.
With a sharp knife, score the fat-side of meat 1/4-inch deep, making in a diamond pattern. Place the pork fat-side up in a roasting pan. Rub the marinade into the pork, making sure to get into all the crevices. Cover tightly with plastic wrap and refrigerate for at least 4 hours or, for best results, overnight.
Preheat the oven to 400 degrees F.
One hour prior to cooking, remove the pork from the refrigerator and let it rest at room temperature. Remove the plastic wrap and set the meat fat-side up on a rack in a deep roasting pan. Cook uncovered for 15 minutes, then lower the heat to 300 degrees F and cook another 3 1/2 to 4 hours, until the internal temperature registers 180 to 185 degrees F and the skin is crispy. (If the pork begins to brown too much on top, cover it loosely with foil.)
Cut away the pork skin (the chicharron), chop it finely, and set aside 1/2 cup for the mofongo. Let the meat rest 20 to 30 minutes before shredding.
For the sopa de pollo: Set a medium saucepan over medium heat and add enough canola oil to coat the pan. Add the onions, peppers and garlic and sweat until translucent and fragrant, 5 to 7 minutes. Sprinkle with salt. Add the chicken and cook for 2 to 3 minutes. Deglaze the pan with the chicken broth. Add 1 cup water, bring to a gentle boil, then simmer over low heat for 30 to 45 minutes. Stir in the cilantro and add salt to taste.
For the mofongo: Preheat the oven to 375 degrees F.
Slice off the top of the garlic head, cutting away just enough to expose the cloves. Set the garlic on a double layer of aluminum foil and drizzle with the olive oil. Sprinkle with salt and pepper. Close the foil tightly to create a pouch, and transfer it to a baking sheet. Bake for 45 minutes, or until the cloves turn golden brown. Let rest until cool enough to handle. Working over a bowl, squeeze the bottom of the garlic head to release the cloves. Set aside.
Set a saute pan over medium-high heat. Add the bacon and cook until crispy and well browned. Transfer to a paper-towel-lined plate to drain.
In a deep pot or Dutch oven, heat 3 inches of oil to 325 degrees F. Working in batches, fry the plantains in the oil until golden and soft, 3 to 4 minutes. Drain on paper towels. When cool enough to handle, smash the plantains with a spatula or the side of a knife, then return them to the oil. Fry a second time, until they're just starting to brown. Drain on paper towels and season with salt as the plantains come out of the oil.
To assemble: In a large, heavy metal mixing bowl, combine the fried plantains, the roasted garlic, the bacon, 1 teaspoon salt, 1/4 teaspoon pepper and the reserved 1/2 cup pork skin, as well as the cilantro, scallions and lime juice. Toss to mix. Season with salt and pepper. Scoop out individual portions of mofongo using an ice cream scoop and transfer to shallow bowls. Ladle some of the sopa de pollo over the top or serve it in small bowls on the side. Top the mofongo with some of the shredded pork. Serve.