Prepare the rabbit filling: Debone front and back legs, discarding any connective tissue; reserve bones. Refrigerate half of the leg meat for later use. Cut remaining meat into 1⁄4" cubes and chill in freezer for 30 minutes. Meanwhile, heat 2 tbsp. oil in a small saucepan over medium heat. Add minced shallots, carrots, and celery and cook, stirring, until soft, 10 minutes; remove from heat and set aside. Transfer chilled meat to a food processor. Pulse to grind meat; add minced shallot mixture along with créme fraíche and egg yolk and process to form a smooth mousse. Season mousse with salt and pepper, transfer to a small bowl, cover, and set aside.
Make the jus: Heat oven to 425º. Set rabbit bones on a rimmed baking sheet and bake, turning once, until golden brown; remove from oven and set aside. In a saucepan, heat 2 tbsp. oil over medium heat. Add sliced shallots, carrots, and celery; cook, stirring, until soft, about 10 minutes. Stir in tomato paste and cook 2 minutes. Add wine and cook, stirring, until evaporated, about 2 minutes. Add peppercorns, rosemary, thyme, and reserved rabbit bones. Add enough water to cover, bring to a simmer; cook, skimming surface occasionally, for 1 1⁄2 hours. Set a fine strainer over a saucepan; strain the broth, discarding solids. Heat broth in saucepan over medium heat and reduce by half. Season jus with salt and set aside; keep warm.
Assemble the rabbit: arrange speck in a rectangle on a sheet of parchment paper so that speck forms a border at least 1" beyond edges of the rabbit saddle. Lay the cabbage leaves evenly over speck. Place rabbit saddle over the cabbage so that inside is facing out. Season rabbit with salt and pepper. Spoon mousse in a 2" stripe down center of rabbit. Put reserved boneless rabbit meat on top of the mousse. Working from one long end, roll up the rabbit, leaving the cabbage and speck on the parchment, to form a roll. Bring the roll to one long end of the cabbage and speck. Starting with the edge closest to the rabbit, roll the speck-and-cabbage layer around the rabbit to form one long roulade.
Transfer rabbit roulade to a long sheet of plastic wrap still attached to the roll; discard the parchment. Roll rabbit tightly in the plastic until several layers have accumulated. Cut plastic wrap and roll rabbit in 3 more layers of plastic wrap. Using your hands, twist both ends of plastic wrap at the same time to form a tight roulade. Tie one end tightly with kitchen twine. Twist and tighten other end and tie it with kitchen twine. Tie another length of kitchen twine around the middle of the roulade.
Bring a 5-qt. pot of water to a bare simmer (140º). Add the rabbit roulade and cook, maintaining temperature of 140º, until set, about 50 minutes. Transfer the roulade to a large bowl of ice water and chill for 10 minutes. Drain and remove the plastic wrap. Working with twelve 10" lengths of kitchen twine, tie the rabbit crosswise at 1" intervals and trim excess twine.
Heat oven to 350º. Heat 2 tbsp. oil in a 12" ovenproof skillet over medium-high heat. Add rabbit and cook, turning occasionally, until browned on all sides. Transfer pan to oven and cook until an instant-read thermometer inserted into center of rabbit reads 150º. Transfer rabbit to a plate and let rest.
Heat remaining oil in a 12" skillet over medium-high heat. Add steamed carrots, radishes, and romesco and cook, stirring occasionally, until golden brown. Season with salt and pepper; set aside. To serve, remove kitchen twine, cut rabbit crosswise into 1" slices, and divide meat between 4 warm serving plates. Arrange vegetables and chestnuts around rabbit and spoon some of the reserved jus over rabbit.