Heat 1 Tbsp oil in a large saucepan. Cook the onion, celery and carrots until onions are translucent and fragrant, around 3-5 minutes. Transfer the vegetables to a plate and set aside.
Add the remaining oil to the saucepan. Cook the mushrooms in the saucepan for around 5 minutes. Add in the garlic, and cook for an additional minute.
Add back the vegetables. Mix in the vegetable broth, heavy cream, thyme and kale. Bring to a simmer, and allow to cook for around 25-30 minutes.
Mix in the cornstarch until the soup thickens. Add in salt and pepper to taste.