Season the chicken pieces with salt to taste. Heat half of the oil (2 tablespoons) in a large skillet and brown the chicken just until the skin looks crispy and nicely golden.
In the remaining oil (drain some of the oil if there's too much), fry the garlic cloves for a couple of minutes or just until it begins to go a lighter brown.
Mix the ground paprika, garlic powder, salt, pepper, and rosemary with the remaining oil (2 tablespoons olive oil) in a large bowl. Add the chicken pieces. Toss to coat.
Place the garlic and oil in a deep oven-safe dish, and then mix in the courgettes or zucchini until they are coated with the oil. Lightly season with a little salt and pepper.