Start by heating a soup pot over medium heat until hot.
Add olive oil and bring to shimmer but Do Not Burn.
Add the onions & garlic and saute until onions are translucent and starting to brown. This will take 8 to 10 minutes.
Add the vegetable stock, cover, and simmer for 10 minutes. You may have to lower the heat at some point.
Add the chicken stock, carrot, squash, and chopped cremini mushrooms. Continue cooking at a simmer until the squash is cooked through - about 15 minutes.
Add the wild mushrooms and barley to the soup and continue to cook until the barley plumps up. This will take about 30 minutes.
Add the chickpeas and kale and continue simmering for another 10 minutes until the barley is soft.
Taste and season with salt and pepper.
Serve in soup bowls topped with a bit of grated Parmesan cheese.