Preheat the oven to 190°C (375°F). Cut each chicken breast horizontally along its length to produce four thinner chicken pieces, helping them cook more quickly and evenly.
Coat the bottom of a casserole dish or oven-safe pan with the vegetable oil. Arrange the chicken portions over the oiled surface, then position the broccoli florets evenly around the meat.
Season the chicken and broccoli with the paprika, mixed herbs, a small pinch of salt, and a generous amount of freshly ground black pepper.
Pour the cream of chicken soup evenly over the chicken and broccoli. For a slightly thinner sauce, stir in or pour over up to 50 ml of chicken stock.
Scatter the shredded mozzarella across the entire casserole, covering the chicken, broccoli, and creamy sauce. Cover the dish securely with kitchen foil.
Bake the covered casserole for 20 minutes. Remove the foil and return the dish to the oven for a further 15 minutes, or until the cheese is bubbling and lightly browned and the chicken is thoroughly cooked.
Allow the casserole to cool briefly after removing it from the oven. Finish with the chopped fresh parsley, if desired, and serve while hot.