Place 2 tablespoons olive oil into stockpot over high heat until the oil shimmers. Add the mushrooms and sauté until browned, about 5 minutes. Remove the mushrooms and set aside.
Decrease the heat to low, add the remaining 2 T olive oil and the carrots, celery, onions, and salt. Cook, stirring occasionally, until softened.
Add the tomatoes, sage, rosemary, and garlic, and cook 5 minutes.
Add the broth, soy sauce and Parmesan rind; bring to a boil, about 15 minutes.
Decrease the heat to low, add the squash and kale, cover and cook until tender, 30 to 35 minutes.
Add the beans, mushrooms and red wine vinegar and cook until heated through, about 15 minutes. Serve with Parmesan cheese.
Notes
In lieu of cherry tomatoes, you can substitute a can of diced tomatoes. To make this vegetarian, use water or vegetable broth instead of chicken broth. Share this soup with your neighbor and spend some time catching up.