Tip:To adapt a slow-cooker recipe to a conventional oven, follow these guidelines: add more liquid, to accommodate for greater evaporation; bring the dish to a boil over high heat in a Dutch oven, then cover the pot and put in a 350°F oven. Plan on the dish taking roughly half the time to cook in the oven as it would in the slow cooker.
Heat the oil in a large heavy saucepan over medium-high heat. When hot, add the shallots, ginger, and jalapeño and sauté until softened, about 2 minutes. Add the cherries, tomatoes, molasses, vinegar, chipotle, 1 Tbs. mustard, 3⁄4 tsp. chile powder, 1-1⁄2 tsp. salt, and 5 grinds pepper, and bring to a boil over high heat. Reduce to a simmer over medium heat, and cook until aromatic and thickened, about 5 minutes. Remove from the heat and carefully transfer half to a blender; purée until smooth, about 20 seconds. Purée the second half until smooth (you should have about 5-1⁄4 cups). Set aside.
Meanwhile, mix 2 Tbs. mustard, 1⁄2 tsp. chile powder, 1⁄2 tsp. salt, 10 grinds pepper, and the brown sugar in a large bowl; add the chicken and mix well with your hands. Put the chicken in the bottom of the slow cooker and pour 1-1⁄2 cups of the barbecue sauce on top (reserve the remainder for serving and extras). Cover and cook on low until the meat is cooked through and tender, 4 to 4-1⁄2 hours.
Use tongs to transfer the chicken to a cutting board and carefully use a fork to separate the meat from the bones, discarding the bones (you should have about 4 cups meat).
To serve, stir together 1 cup of the remaining sauce and the shredded meat, and reheat in the microwave or on the stovetop. Spoon some meat and sauce onto the bottom half of each bun, cover with the top bun, and serve.