For the pulled pork, combine ancho chile powder, paprika, coriander seeds, cumin and salt in small bowl; set aside. Cut two large pieces of plastic wrap. Place plastic wrap pieces on work surface in a cross position. Place roast on top in the center. Rub 2 teaspoons of oil on top of roast; spoon and pat half of the spice mixture on top. Carefully turn over roast on plastic wrap. Rub 2 teaspoons of oil on top; spoon and pat on the remaining spice mixture. Tightly wrap pork in the plastic wrap. Refrigerate for 8 to 12 hours. Preheat oven to 300° F. Add the remaining 2 tablespoons of oil to a 6-quart heavy Dutch oven. Heat over medium-high heat. Unwrap roast and place in hot oil in Dutch oven. Cook on each side for 1 to 2 minutes or until spices begin to brown and appear slightly dry. Transfer roast to a plate. Remove Dutch oven from the heat. Slowly and carefully pour in beer, scraping brown bits from bottom of pan. Add water, vinegar, chipotle peppers, onion and garlic. Return to heat; bring to a gentle boil. Add the pork roast to the hot liquid. Cover and bake in preheated oven for 2 1/2 to 3 hours or until pork is fork tender. Transfer pork to a cutting board; cool slightly. Meanwhile, pour liquid through a fine mesh strainer; reserve 1 1/2 cups. Discard remaining liquid and solids. Shred meat using 2 forks; transfer to a medium container. Add the 1 1/2 cups reserved liquid. Cover and refrigerate until ready to use or for up to 2 days.

Form the ground pork into six half-inch-thick patties. Season both sides of patties with salt and pepper. Preheat grill to medium hot. Place pulled pork in a pot and place on the corner of a grill to keep warm. Place patties directly over heat. Grill, uncovered, for 8 to 10 minutes or until pork patties reach 160 degree internal temperature, turning patties over halfway during grilling. In the meantime, toast the buns on the grill. Top the pork patties with cheese. Cover grill and grill about 30 seconds or until the cheese is melted. Place burgers on bun bottoms. Using a slotted spoon, spoon pulled pork on top of burgers. Top with onions, cilantro and bun tops. Eat immediately!