1. Heat the olive oil or butter in a large pot or Dutch oven. Add the fennel and onions. Season them with salt and pepper, cover, and let cook for about ten minutes, lifting the lid and stirring every few minutes, until the fennel and onions are cooked through.
2. Add the pear pieces and cook for another few minutes, until they’re soft and tender.
3. Pour in the cider and the water, and add the bay leaves, then cover and let cook until the liquid comes to a boil. Reduce heat and let cook over low heat with the lid ajar for 5 to 10 minutes.
4. Pluck out the bay leaves, then blend the soup; if using a stand blender, let the soup cool down until it’s tepid before blending, or use an immersion blender.