1. Heat the oil and butter over medium heat in a skillet or Dutch oven large enough to hold the sprouts in a single layer. Add the sprouts and cook, turning often, until they are lightly browned.
2. Add the thyme, garlic, salt and pepper and cook one minute. Add the lemon zest and the stock and reduce the heat slightly. Cover and cook the sprouts until they are tender, about 10 minutes (or longer if they are larger sprouts), adding additional stock if you need to.
3. When the sprouts are cooked, add the walnuts, toss and cook for another minute or two, and serve.