In a large saucepan over medium heat, heat the olive oil and butter until the oil is shimmering and the butter is melted, about 2 minutes. Add the onion and carrots and saute until the onions are tender, 5 to 8 minutes. Add the mushrooms and rice and cook for 5 minutes more, toasting the rice. Add the garlic.
Add the stock. Bring the mixture to a boil, then reduce the heat to low. Add the kale and kohlrabi, cover and simmer until the wild rice is tender, about 20 minutes. Season with salt and pepper to taste.
Some of the stock will be absorbed into the rice as it cooks. Add more stock and heat through before serving if necessary.