Warm the vegetable broth (or vegetable broth + water) in a medium-sized saucepan over medium-low heat.
Heat a large pan over medium heat. Once heated, add 1 tbsp olive oil and mushrooms. Cook until the mushrooms are browned and are releasing some of the liquid, about 3-4 minutes. Remove the mushrooms and their liquid and set aside.
Reheat the same pan over medium heat. Add 1 tbsp olive oil and diced onions. Saute until onions are translucent, about 4 minutes. Add garlic and saute for an additional minute.
Add the arborio rice to the pan and cook for 1-2 minutes, stirring occasionally to coat the rice with the oil.
Add the wine and cook until the liquid is absorbed, about 1-2 minutes.
Begin adding the warmed vegetable broth ½ cup at a time to the rice mixture and stir, letting the rice absorb the broth between each addition. Repeat until the rice is al dente, or until desired texture is achieved. This step takes approximately 20 minutes to complete.
Add mushrooms and their liquid to the rice and mix them together. Salt and pepper to taste.
When ready to serve, mix in the walnuts and garnish with fresh parsley and more walnuts. Only add the walnuts at the time of serving. If preparing ahead of time, do not add walnuts until serving.