Add the oil to a 10-inch paella pan on medium heat. Add the rabbit ribs and chicken thighs, seasoning them with salt. Sauté until golden brown on both sides, about 8 minutes. Add the paprika and a pinch of saffron and sauté until fragrant for about 5 minutes. Next add the garlic, green beans, runner beans, artichoke hearts, and tomato sauce.
Meanwhile, add the rest of the saffron to the chicken broth. That way the saffron can steep while the veggies, chicken and rabbit are continuing to sauté for about 6 minutes on medium-low heat.
Pour in 2 cups of the saffron-infused chicken broth and simmer on low uncovered for 20 minutes.
Add the rice to the paella pan laying it out in an X shape. Maria explained that this gesture was important and a tradition her grandpa did while laying the rice out evenly in the pan. Add the remaining chicken broth.
Lay the rosemary sprig on top of the rice. This will perfume the rice and be easy to pull out later. Cover the rice with a lid and cook on low for 20 minutes.
Take the paella off of the heat and cover it with a damp towel and no lid. Let the paella rest for 5-10 minutes. Pull out the rosemary sprig before serving and enjoy hot.