In a Dutch oven over medium heat, warm the olive oil. Add the leeks, celery, and a pinch of salt, and sauté until softened, about 5 minutes. Add the rice and toast for a minute.
Add the broth and bring to a boil. Cover, reduce to a simmer, and cook for 40 to 50 minutes, or until the liquid is absorbed. If rice is cooked but some liquid remains, drain. Transfer rice to a large bowl.
While the rice cooks, prepare the mushrooms. In a large skillet over medium heat, warm 2 tablespoons olive oil and the minced garlic. Add the mushrooms, thyme, and a pinch more salt and pepper. Cook, stirring occasionally, until nicely browned, about 12 minutes. Add more olive oil, if needed. Transfer to the bowl with the rice and add most of the parsley, reserving some for garnish, lemon zest, and toasted walnuts. Mix well to combine.
Preheat oven to 350°F. Transfer the rice mixture back into the Dutch oven, cover, and bake for 25 minutes. Uncover and bake until lightly browned, about 10 minutes more. Finish with remaining parsley and serve.
This nutritional information refers to each serving of the entire recipe and not just the products used as ingredients.