Heat the oil and butter together in a skillet over medium heat; saute onion and garlic till onion is translucent; add mushrooms and cook till well wilted and browned, about 10 minutes.
Transfer mixture to a slow cooker; add chicken broth and season with salt and pepper.
Cover and cook on low heat setting for 5 to 7 hours. Add the half and half during the last hour and serve when nice and hot.