Lay 2 sheets 24 inches long of heavy duty foil down in a cross pattern then lay the collard greens on the foil in the cross pattern. Douse the pork with olive oil to coat then add 2 tablespoons Spanish paprika and 1 tablespoon pimenton paprika, liquid smoke, and salt and pepper. Place pork in mound over collards then pull the leaves over the top of the pork and wrap the package securely. Place on a sheet pan and put into the oven. Bake for 2 1/2 hours. Remove from oven, open package to allow steam to escape and reserve.
Heat more oil and butter in a medium ovenproof skillet over medium heat. Add garlic and cook 1 minute then add chorizo and onion. Cook until softened 7 to 10 minutes. Then add piquillo peppers, sweet paprika, remaining 1 tablespoon smoky paprika, saffron, and oregano, cook 1 minute. Then add green chiles, tomatoes and stock. Bring to a boil and simmer 5 minutes. Add thyme and beans and cook 5 more minutes. Add cooked pork with broth from foil pack, cook 5 more minutes. Turn off heat and add chopped parsley.