Preheat the oven to 325 degrees F (165 degrees C).

Heat olive oil in a Dutch oven over medium-high heat until shimmering. Add chicken and cook until well browned, 3 to 4 minutes per side. Remove to a plate.

Reduce heat to medium and add bell pepper, onion, celery, carrot, and garlic. Sauté until translucent, about 5 minutes. Add tomato paste and stir to blend into the vegetables.

Add crushed tomatoes, wine, allspice, bay leaf, seasoning sauce, salt, and pepper. Return chicken to the pan and toss to coat all pieces.

Cover the Dutch oven and place in the preheated oven. Braise until chicken is falling off the bone and the juices run clear, 1 1/2 to 2 hours. An instant-read thermometer inserted near the bone should read 165 degrees F (74 degrees C).