Preheat the oven to 450 degrees F.
For the barbecue pork: In a medium saucepan, heat the oil until shimmering. Add the onion and cook until tender, about 5 minutes. Add the butter and garlic and continue to cook until the garlic is softened. Add the ketchup, molasses, vinegar, hot sauce, mustard and brown sugar and simmer until the sugar is melted and the ingredients have combined, about 5 minutes. Transfer to a blender and carefully blend until smooth. Return to the pan, add Trisha's Pulled Pork and keep over low heat to warm through.
For the cheese sauce: Heat the cream and pepper in a small saucepan over low heat until it just begins to steam, about 3 minutes. Gradually add the cheese, stirring until the cheese is completely melted. Keep warm, adding a bit more cream if the sauce becomes too thick.
For the nachos: In a shallow casserole dish, spread the shredded romaine and then top with the tortilla and potato chips mixed together. Spread the pork over the chips and cover with the shredded Cheddar. Bake until the cheese has melted, 8 to 10 minutes. Pour the cheese sauce over top and garnish with the red onions and scallions.
Season the ribs well on all sides with salt and pepper.
In a large Dutch oven over high heat, heat the oil to a shimmer. Add the ribs and sear until browned on all sides, about 8 minutes. Remove the ribs and transfer to a plate. Add the garlic, carrots and onion and cook until golden and caramelized, about 10 minutes. Add the tomato paste and cook for 2 minutes. Add 1 cup of water and, using a wooden spoon, scrape up any browned bits from the bottom of the pan. Add 2 more cups of water and stir to combine.
Return the ribs to the Dutch oven, cover and reduce the heat to low. Cook until fork-tender, about 3 hours.
Remove the ribs from the liquid and transfer to a baking sheet to cool. Strain the cooking liquid and reserve. When cool enough to handle, use 2 forks to shred the pork.
When blending hot liquid, first let it cool for five minutes or so, then transfer it to a blender, filling only halfway. Put the lid on, leaving one corner open. Cover the lid with a kitchen towel to catch splatters, and pulse until smooth.