Melt 1 tablespoon butter with 1/2 tablespoon olive oil in saucepan over medium heat. Add onions and saute, stirring every few minutes, until they are caramelized, about 15-20 minutes. Add the mushrooms, celery, carrot, garlic and salt, and saute, stirring occasionally, for a further 5 minutes. Add chicken stock, thyme (or herbes de provence) and bay leaf to saucepan. Reduce temperature to a slow boil and cook, covered, for 15-20 minutes longer, or until vegetables are tender. Remove from heat. Discard bay leaf.
(Carefully) blend soup in batches, either in blender, or using immersion blender, until soup is mostly pureed, leaving a bit of texture in the vegetables. Return to saucepan and over a low heat, whisk in half and half, ricotta and swiss cheeses, until cheeses have entirely melted into the soup. (If soup is too thick, thin with a little more hot broth). Season to suit your taste with salt and freshly-cracked black pepper.
Serve in deep bowls, garnished with a sprinkle of minced, fresh parsley.