Sprinkle rabbit pieces with 1 teaspoon salt and ½ teaspoon pepper; dredge in ½ cup flour, shaking off excess.
In a large Dutch oven, heat oil over medium-high heat. Add half of rabbit; cook until browned, 2 to 3 minutes, turning occasionally. Remove from Dutch oven. Repeat with remaining rabbit. Add onion, celery, and bell pepper to Dutch oven; cook until softened, about 2 minutes. Add tasso and garlic; cook 1 minute. Add reserved rabbit, wine, chicken broth, and bay leaves. Bring to a boil; cover, reduce heat, and simmer 1 hour.
Add carrot, mushrooms, potato, thyme, rosemary, sage, remaining ½ teaspoon salt, and remaining ½ teaspoon pepper. Bring to a boil; cover, reduce heat, and simmer until tender, about 40 minutes more.
In a small bowl, place remaining 2 tablespoons flour. Whisk in 3 tablespoons cold water and tomato paste. Stir into stew; cook until thickened, about 5 minutes. Discard bay leaves. Garnish with thyme and parsley, if desired.
Notes
*1 (4-pound) chicken, cut into 8 serving pieces, may be substituted. We used Pinot Noir.
Recipe by Louisiana Cookin' at https://louisianacookin.com/rabbit-vegetable-stew/