You may need to do this in batches. Cook on one side for 3-4 minutes and repeat on the other side. Remove the pieces to the plate with the chorizo. Cook the rabbit the same way. Next add the diced onion and garlic. Cook for 2-3 minutes or until the onions begin to soften, stirring occasionally. Add the rice, making sure to stir well, coating with the oil for 2 minutes or until it becomes opaque. Add in the tomatoes and bay leaves, stirring to combine. Remove the whole onion from the broth. Pour in 3/4 of the broth. It should cover the the rice completely. Let the mixture boil for about 5 minutes, stirring to scrape up any crispy bits off of the bottom.
Nestle the chicken, rabbit and chorizo into the rice. Cover and cook for 15 minutes. Add the remainder of the broth, shrimp, clam/mussels and arrange the pepper strips on top, sprinkling with the olives. Cover and let cook for 5-10 more minutes. The rice on top should be a bit “al dente”.
Remove from heat, recover and let sit for 5-7 minutes. Sprinkle with parsley and serve family style. You should have a layer of crispy toasted rice at the bottom of the pan, called “socarrat”.