In a heavy pot or Dutch oven, heat olive oil over medium. Add onion, carrot, garlic, and mushrooms. Sauté until onions are translucent, about 15 minutes.
Add marjoram, thyme, vegetable broth, and orzo pasta. Bring to a simmer and cook until pasta is halfway done, about 6–7 minutes.
In a small bowl, whisk together flour and heavy cream until smooth. Pour into the soup, stirring constantly.
Cook for an additional 10 minutes, until the soup begins to thicken.
Add bay leaf, salt, and pepper to taste. Turn off the heat and let the soup sit for 5 minutes before serving.
Serve hot and enjoy!