Rinse and pat dry rabbit loins. In a mixing bowl, stir together cold water, vinegar, salt and peppercorns. Place rabbit loins in liquid and allow to stand 1 hour. Remove rabbit from brine and pat dry.
In a 12- to 14-inch heavy bottomed saute pan, heat 4 tablespoons olive oil until smoking. Season rabbit pieces with salt and pepper and saute until golden brown on both sides, about 6 to 7 minutes. Remove rabbit pieces and set aside. Add fennel, onion and fennel seeds and cook until soft and lightly browned, about 10 minutes. Add tomato sauce, wine and balsamic vinegar and bring to a boil. Place rabbit pieces in pan and simmer 15 minutes uncovered.
Meanwhile, make salsa verde. Soak bread in white wine vinegar about 2 minutes. Remove bread from vinegar and squeeze dry. Place in food processor with parsley, capers, garlic, spinach, thyme, fennel fronds and extra virgin olive oil. Blend 30 seconds until smooth and set aside. Remove cooked rabbit pieces from sauce and arrange on a serving platter. Top with fennel sauce mixture, drizzle with salsa verde and serve immediately.