Pour vegetable broth in a large pot and bring it to boil.
While the broth is warming up, heat the olive oil on a large skillet. Sauté onion till golden, add the carrots, garlic, and asparagus and sauté until soft.
Once the broth is boiling, add potatoes and cook for about 5 minutes, add the sautéed mixture, and cook for another 5-7 minutes until potatoes are well cooked.
Collect about 1/3 of the vegetables and puree them in a food processor. Return the puree into the soup pot. Add mushrooms and bay leaves, and simmer on low heat for 10 more minutes. Add salt and pepper.
The soup tastes even better on the second day.
Serve hot with sour cream and freshly chopped dill.
Make ahead: this soup freezes well for up to 6 months. Pour chilled soup (without sour cream and dill) into a large zip lock bag. Lock it, squeezing the air out. Lay flat in the freezer.