Heat olive oil in a large pot over medium heat.
Add diced onion and sauté for 5 minutes until translucent.
Add minced garlic and cook for 1 minute until fragrant.
Add sliced mushrooms and cook for 7-8 minutes until they release their moisture and start to brown.
Sprinkle the flour over the mushrooms and stir well to coat. Cook for 1-2 minutes to remove the raw flour taste.
Slowly pour in the vegetable broth while stirring to avoid lumps.
Add chopped kale, dried thyme, salt, black pepper, and smoked paprika. Stir to combine.
Bring the soup to a boil, then reduce heat to low and simmer uncovered for 15 minutes until the kale is tender.
Stir in the heavy cream and cook for an additional 5 minutes, stirring occasionally, until heated through.
Taste and adjust seasoning if needed.
Serve hot.