Bring a 3-quart / 2.8 L saucepan of water to a boil. Add the pearl onions and boil for 2 minutes, then drain and rinse under cold water. Trim only the stem end of each onion, leave the root end on, and squeeze the onion out of its skin.
Pat the rabbit dry and season with 1 tsp of the salt and the pepper. Heat 3 tbsp of the oil in a 28 cm / 11-inch (5-quart / 4.7 L) Dutch oven over medium-high heat. Brown the rabbit in two batches of 4 pieces, 3 to 4 minutes per side, until deep golden, about 15 minutes total. Move the pieces to a plate.
Lower the heat to medium and add the remaining 1 tbsp oil. Add the pearl onions and cook for 5 minutes, stirring, until the edges look lightly golden. Stir in the garlic and tomato paste and cook for 1 minute, until the paste darkens.
Pour in the wine and vinegar, scraping the browned bits off the bottom with a wooden spoon. Simmer for 3 minutes, until the liquid reduces by about a third and the sharp vinegar smell softens.
Add the crushed tomatoes, water, bay leaves, cinnamon stick, cloves, allspice and the remaining 1/2 tsp salt. Return the rabbit and any juices from the plate, nestling the pieces among the onions. Bring to a gentle boil, then lower the heat to a bare simmer, around 95 C / 203 F, cover, and cook for 60 minutes. Rabbit is lean, so if the sauce boils hard the meat turns dry and stringy. Turn the heat down if you see big bubbles.
Uncover and simmer for 20 more minutes, until the sauce coats the back of a spoon and the onions are soft but still whole. The rabbit is safe at 160 F / 71 C, but here you want it well past that, when the meat pulls easily from the bone. Remove the bay leaves and cinnamon stick.
Turn off the heat, cover the pot, and let the stew rest for 10 minutes. Taste, add a pinch more salt if needed, and sprinkle with the parsley before serving.