Melt 2 tablespoons unsalted butter in a Dutch oven over medium heat. Add 1 diced small yellow onion and cook until translucent, about 3 minutes. Stir in 3 minced garlic cloves and cook until fragrant, about 1 minute.
Stir in 1 (32-ounce) carton low-sodium chicken broth, 1 pound peeled and diced Yukon gold potatoes, 1 (14.5-ounce) can diced tomatoes and their juices, 1 cup frozen lima beans, and 1 cup frozen corn kernels. Bring to a boil over medium-high heat.
Reduce the heat to maintain a simmer. Cover and cook until the potatoes are tender, about 10 minutes.
Stir in 1 pound shredded pulled pork, ¼ cup barbecue sauce, 1 tablespoon apple cider vinegar, 1 tablespoon smoked paprika, 1 tablespoon Worcestershire sauce, 1 teaspoon kosher salt, and ½ teaspoon black pepper. Bring back to a simmer and cook uncovered until the flavors meld, about 10 minutes. Taste and season with light brown sugar, barbecue sauce, kosher salt, or black pepper as needed.
