Authentic Paella Valenciana

Name: Authentic Paella Valenciana
Ingredients: 1 tablespoon olive oil; 0.5 (4 pound) whole chicken, cut into 6 pieces; 0.5 (2 pound) rabbit, cleaned and cut into pieces; 1 head garlic, cloves separated and peeled; 1 medium tomato, finely chopped; 1 (15.5 ounce) can butter beans; 0.5 (10 ounce) package frozen green peas; 0.5 (10 ounce) package frozen green beans; 1 teaspoon mild paprika, or to taste; 6 cups water, or as needed; salt to taste; 1 pinch saffron threads, or to taste; 1 pinch dried thyme, or to taste; 1 pinch dried rosemary, or to taste; 3 cups short-grain white rice, or as needed