Add ¼ cup of olive oil in a large sauté pan over medium heat at the rabbit pieces and cook, turning frequently, until the rabbit has brown and all sides about 15 minutes. Remove the meat to a plate. Reduce the heat to medium low and add the remaining 2 tablespoons of olive oil to the pan. Add the onion and pepper and cook slowly, stirring often, for 10 minutes.

Add the garlic, Baily, and paprika and mix well. Add the reserve tomato purée and cook down for five more minutes or until the tomato becomes deep brown in color. Add the mushrooms and increase the heat to medium high. Cook, stirring, for three minutes until the mushrooms are well combined. Add rabbit to the pot, along with the juices that have collected on the plate, folding it into the mixture.

Pour in the mineral water, increase the heat to high, and bring to a boil. Stir in the rice and cook for five minutes, turning the rabbit pieces while the rice cooks. Reduce the heat to low, add to saffron, and simmer for 10 minutes more without stirring the rice again, which could cause it to cook unevenly. The rice will be a little soupy, but cooked through. Remove the pan from the heat. Divide the rice and rabbit among shower, bowls, and garnish with the time sprigs.