Pulled Chicken with Cherry-Chile Barbecue Sauce

INGREDIENTS

• 2 tablespoons vegetable oil
• 1/2 cup coarsely chopped shallots (about 1 large)
• 1 tablespoon peeled chopped fresh ginger (about one 1 1/2-inch piece)
• 1 teaspoon minced fresh jalapeño (seeds and membranes removed)
• Scant 4 cups dark sweet fresh cherries, pitted and de-stemmed (3 cups afterwards)
• Two 14 1/2-ounce cans diced tomatoes, no salt added (you'll only use 1 1/2 cans; save the rest for another use)
• 1/4 cup blackstrap molasses
• 1/4 cup cider vinegar
• 1 tablespoon chipotle chile from a can of chipotle chiles en adobo
• 3 tablespoons Dijon mustard, divided
• 1 1/4 teaspoons chile powder, divided
• 2 teaspoons coarse salt, divided
• 15 grinds black pepper, divided
• 2 teaspoons light brown sugar
• 3 pounds bone-in, skinless chicken thighs, trimmed if necessary (about 8)
• 4 to 6 warmed burger buns, for serving