Preheat your oven to 325°F (163°C).
Season the ostrich neck fillets with salt and pepper on both sides.
Heat the olive oil in a large oven-safe pot or Dutch oven over medium-high heat. Brown the ostrich neck fillets on all sides until they develop a golden crust. Remove the fillets from the pot and set them aside.
In the same pot, add the chopped onion, carrots, celery, and minced garlic. Sauté for a few minutes until the vegetables begin to soften and turn slightly golden.
Deglaze the pot by adding the red wine and scraping the bottom to release any browned bits. Allow the wine to simmer for a couple of minutes to reduce slightly.
Return the ostrich neck fillets to the pot and pour in the broth. Add the fresh thyme sprigs and season with additional salt and pepper if desired.
Cover the pot with a lid and transfer it to the preheated oven. Allow the ostrich neck to braise for approximately 2 to 2 ½ hours or until the meat becomes tender and easily pulls apart.
Once the ostrich neck is cooked, remove the pot from the oven and let it rest for a few minutes.
Serve the braised ostrich neck fillets with the vegetables and some of the cooking liquid as a sauce. You can pair it with mashed potatoes, rice, or roasted vegetables.This braised ostrich neck recipe provides a flavorful and tender result. Remember to adjust the cooking time if you're using larger or smaller ostrich neck fillets. Enjoy your meal!