Make the seasoning mix: Combine the paprika, sugar and onion powder in a small bowl. Store in an airtight container for up to 6 months.
Make the barbecue spaghetti: Combine the ketchup, both sugars, 1 1/2 teaspoons pepper, the onion powder, mustard powder, lemon juice, Worcestershire sauce, cider vinegar, 1/3 cup seasoning mix and 1 cup water in a large pot or Dutch oven. Bring to a boil over high heat, stirring frequently to prevent the sauce from sticking to the pot. Reduce the heat to low and simmer, uncovered, 1 hour.
Heat the olive oil in a large skillet over medium-high heat. Add the bell pepper and onion and cook, stirring, until the vegetables soften, about 5 minutes. Add the sauteed vegetables and pulled pork to the sauce and continue to simmer, 1 more hour.
Bring a large pot of salted water to a boil. Cook the spaghetti as the label directs. Drain, then add to the pot with the sauce and toss.
Photograph by Yunhee Kim
Recipe courtesy Patrick and Gina Neely for Food Network Magazine