- In a saucepan, bring stock to a light simmer and add parsley and thyme. Reduce heat to very low and keep warm.
- Warm a separate large saucepan over medium heat. Add butter and oil. When butter has melted, add onion and sauté until translucent, about 10 minutes. Add celery and sauté until softened, about 5 minutes. Add gizzards and sauté until cooked through, about 15 minutes.
- Add rice and stir until it begins to give off a nutty aroma, about 30 seconds. Stir in wine and cook until slightly reduced. Ladle about 1 cup of stock into the pan and cook, adding stock about 1 cup at a time, until rice is tender but the center of each grain is still slightly firm, about 15–20 minutes.
- Remove risotto from heat and stir in half of the cheese. Divide risotto among warmed shallow bowls and garnish with remaining cheese. Serve immediately.