To assemble the nachos, arrange the tortilla chips on a large serving platter. Pile with warm pulled pork. Drizzle barbecue and cheddar sauce over the top, to taste. Garnish with pickled jalapenos and crumbled queso fresco. Serve with cilantro-sour cream, salsa verde and hot sauce on the side.
Preheat oven to 325 degrees F.
First, make the spice rub. Whisk together the paprika, kosher salt, black pepper, garlic powder, chili powder, mustard powder and cayenne. Massage the spice rub into the pork butt, coating on all sides.
Place the rubbed pork in a large Dutch oven; add beer, cider vinegar, and liquid smoke. Cover and cook for approximately 3 hours, basting occasionally, until the pork easily falls apart. Remove the pork to a large cutting board while still hot. Cut off excess fat and carefully shred the meat; it is harder to pull once it has cooled. (I either wear heavy-duty rubber gloves on my hands or use my new "bear paws," but two large forks would work, too.) Place the shredded pork back into the Dutch oven and toss with its cooking juices. Cover and set aside until moving forward with the recipe. Yields: 1 to 1/2 to 2 pounds pulled pork, depending on the amount of fat and bone on the cut.
To reheat, cook the barbecue (in its Dutch oven) over medium-low heat until warm. If you want crispier shredded pork (more like your favorite barbecue house), reheat it on the stovetop first, then spread it on a sheet pan and pop it under the broiler for a few minutes, watching carefully so it does not burn.
In a small saucepan, melt the butter over medium heat. Add the remaining ingredients, whisking to combine. Bring the sauce to a boil; reduce heat and simmer. Cook until the mixture is thickened, approximately 10 minutes. (This barbecue sauce only gets better with time, so feel free to make it a few days in advance.)
In a medium saucepan, whisk together the eggs and evaporated milk. Turn heat to medium-low; add mustard powder, Worcestershire sauce, hot sauce and half of the shredded cheese. Once the cheese sauce begins to warm, add the cornstarch-water mixture (aka the slurry). Whisking frequently, gradually add the remaining cheese and cook until the sauce reaches desired thickness, 10 to 13 minutes. (The sauce will continue to thicken as it cools. Stir in more evaporated milk if necessary.) Season generously with kosher salt. To reheat the cheddar sauce, add additional evaporated milk to the cheese - one tablespoon at a time - while whisking over medium-low heat until desired consistency is reached.
In a small bowl, mix the sour cream, cilantro and lime juice until well combined. Season with salt, to taste. Chill for at least one hour before serving. Add more lime juice and salt before serving, if desired.