Heat the olive oil and butter together in a large stockpot over medium heat. Add in the sliced mushrooms and sauté until golden brown and crispy. Remove from the pot and set aside.
Add in the onion, garlic, and carrots and sauté until soft and aromatic, about 5 minutes.
Pour in the wine to deglaze the pan and be sure to scrape up any browned bits on the bottom. Then add in the vegetable stock.
Add in the wild rice, thyme, sage, salt, pepper, and cayenne.
Bring the soup up to a boil, then cover, reduce the heat and let simmer for about 15 minutes.
Then add in the shredded chicken and continue to cook for another 10-15 minutes, until the chicken is warmed through and the rice is tender. Note: If using raw chicken breasts, simmer until the chicken is fully cooked through (15-20 minutes). Then remove and shred.
Add in the heavy cream, kale, and crispy mushrooms and simmer for another 5 minutes until the kale is just cooked.
Taste and adjust seasonings as needed.
Remove from the heat and serve immediately!
Notes
Since the rice will absorb the broth, I suggest straining out the broth to store separately! Then just combine again before reheating! This is the easiest way to prevent the rice from absorbing all the liquid while it sits in the fridge. Store separately in the fridge for up to 5 days.