Cut the rabbit into manageable pieces. Season generously with salt and freshly ground black pepper.
Heat olive oil and butter in a large skillet or Dutch oven over medium-high heat. Brown the rabbit pieces in batches on all sides, ensuring not to overcrowd the pan. Remove and set aside.
In the same skillet, sauté the chopped onion, carrots, celery, and minced garlic until the vegetables are softened and fragrant, about 5-7 minutes.
Sprinkle flour over the vegetables and stir well to coat. Cook for 2 minutes, stirring constantly, to eliminate the raw flour taste and create a roux.
Deglaze the skillet with white wine, scraping up any browned bits from the bottom of the pan. This adds depth of flavor to the sauce. Add the chicken stock and thyme sprigs, stirring to combine.
Return the rabbit pieces to the skillet. Bring to a simmer, then cover and reduce heat to low. Simmer gently for 1.5 hours, or until the rabbit is very tender and easily falls off the bone.
Stir in the cream and gently simmer for another 5 minutes to slightly thicken the sauce. Taste and adjust seasoning with additional salt and freshly ground black pepper if necessary.
Serve the rabbit fricassee hot, garnished with freshly chopped parsley. Excellent served with rice, mashed potatoes, or crusty bread to soak up the delicious sauce.
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