Heat oil in a heavy pot with a tight-fitting lid over medium-high heat. Season chicken with salt and pepper, brown in batches, 3 minutes per side. Set aside.
In the same pot, layer onion, tomatoes, garlic, and ginger.
Nestle browned chicken pieces on top of the vegetables.
Pour broth around (not over) the chicken, and scatter fresh herbs generously across everything.
Cover tightly, reduce heat to low, and cook undisturbed 45–50 minutes until the chicken is completely tender.
Season with salt and pepper, and serve hot with the vegetables and juices spooned over.