Heat olive oil in a large skillet over medium-high heat. Season the chicken shanks with salt and pepper, then sear them in the skillet until golden brown on all sides. Set aside the browned shanks.

In the same skillet, add the chopped onion, minced garlic, diced carrots, and chopped celery. Sauté until the vegetables turn tender and release their aromas, infusing the dish with rich flavors.

Return the chicken shanks to the skillet. Pour in the chicken broth and red wine, allowing the shanks to be partially submerged. Add fresh rosemary sprigs for an aromatic touch. Cover the skillet and simmer on low heat for about 2 hours until the chicken becomes tender and succulent.