To make the marinade, combine roasted red pepper paste, minced garlic, olive oil, lemon juice, paprika, cumin, allspice, turmeric, salt, and black pepper. Mix well to combine.
Add bone-in chicken to the marinade, ensuring each piece is thoroughly coated, and let it sit for at least 15 minutes or up to several hours in the refrigerator.
Preheat the oven to 360°F (182°C).
Once ready to cook, add cut-up yellow potatoes or baby potatoes to the dish, filling any gaps around the chicken. Pour in chicken broth to come partway up the potatoes and chicken, then place fresh thyme sprigs on top of the chicken and potatoes.
Bake in the preheated oven for approximately 1 hour to 1 hour and 30 minutes, flipping the chicken halfway through cooking. If using, add broccoli in the final 15 minutes so it becomes tender-crisp.
When the chicken and potatoes are cooked through and nicely browned, remove from the oven, top with fresh parsley if desired, and finish with a drizzle of pomegranate molasses.
