Heat stock in a saucepan over medium heat, keeping it at a low simmer.
Heat the oven to 350°F. Spread walnuts in a single layer on a parchment-lined baking sheet. Roast for 5 to 10 minutes, and up to 12, tossing the nuts around occasionally to ensure even cooking. You’ll know the nuts are done when they appear a shade darker and smell toasty. Set aside.
Heat 2 tablespoons of olive oil in a heavy-bottomed saucepan over medium heat. Add mushrooms and cook for 3 to 5 minutes until slightly browned. Remove cooked mushrooms from the pan and place them on a plate. Season with salt and pepper.
Heat olive oil in the pan and add shallots. Cook, stirring, until translucent.
Add the rice and continue to cook, stirring frequently with a wooden spoon for 3 minutes. Add wine to the rice mixture and cook, stirring, until the rice fully absorbs the wine.
Ladle enough of the hot chicken stock over the rice to barely cover it (about ½ cup). Continue to cook, stirring, until the stock is absorbed. Add more stock to cover the rice and stir continuously as the rice absorbs the stock. Repeat this process until most of the stock is absorbed and the rice is cooked with a perfectly al dente center. You may not need all of the stock, so taste the rice frequently to determine when it’s done.
Remove from heat. Stir in butter and Parmesan cheese.
Add walnuts and kale and stir to combine. Gently fold in the mushrooms. Divide the mixture among four shallow bowls and serve immediately.