Heat olive oil in a large saucepan over medium heat until shimmering. Cook and stir celery, carrot, and onion in the hot oil until lightly browned, about 10 minutes. Add jalapeno peppers and cook until fragrant, about 2 minutes. Stir chicken stock, ketchup, vinegar, molasses, brown sugar, and mustard into the vegetable mixture; cook until reduced to about 3 cups, about 30 minutes.
Pour the sauce into a blender no more than half full. Cover and hold lid down; pulse a few times before leaving on to blend. Puree in batches until smooth. Season the sauce with salt.
Preheat grill for medium heat and lightly oil the grate.
Grill the ribs over moderate heat, turning regularly, until crusty and sizzling, about 10 minutes. Brush generously with the barbecue sauce and grill, turning, until deeply glazed, about 5 minutes longer. Serve the ribs with remaining sauce on the side.