Preheat oven to 275°F.
Place rabbit pieces in a heavy pot or Dutch oven. Add duck fat, onion, garlic, fennel seed, peppercorns, 2 teaspoons of the herbes de Provence, orange zest, and bay leaf. Add just enough water or stock to barely cover the meat.
Transfer to the oven and cook for about 2–3 hours, until the rabbit is very tender and falling from the bone.
Remove the rabbit and allow it to cool slightly. Pull the meat from the bones. Break it into coarse pieces with your fingers, keeping some small chunks rather than finely shredding.
Strain the cooking fat and reserve.
Place the warm meat in a bowl and mix in ½–¾ cup of the cooking fat, stirring until the mixture becomes moist and spreadable.
Season with the final teaspoon of herbes de Provence and kosher salt to taste (make it a little saltier than you prefer, as it will be served cold which can mute flavors).
Stir in lemon juice, parsley, and olives. Pack into jars or a small crock and smooth the top. Pour a thin layer of melted fat over the surface to seal. Refrigerate at least overnight, or up to 5 days before serving. Serve with warm bread, crackers, pickled vegetables, or cornichons with a small pinch of flaky salt.
