Heat olive oil in a saucepan over medium heat. Add onions, mushrooms, and garlic; cook and stir until onions soften, about 5 minutes. Add asparagus, wine, thyme, and black pepper; cook and stir until asparagus is tender, about 5 minutes. Pour in 2 cups broth. Simmer soup until flavors combine, 5 to 10 minutes.
Puree soup with an immersion blender until smooth. Stir in cream. Thin soup with remaining stock to desired consistency and simmer until heated through, 5 to 10 minutes.