Melt 4 tablespoons butter in a large pot over medium-low heat and add the onion, apples, potato and squash. Season with salt and pepper and cook until the onion is soft, about 8 minutes. Stir in the sage and flour. Add the cider and cook over high heat, stirring, until thickened. Add the broth and milk, cover and bring to a boil; reduce to a simmer and cook, stirring, until the potato is soft, 8 to 10 minutes.
Meanwhile, heat the remaining 1 tablespoon butter in a large skillet over medium-high heat. Add the prosciutto and cook until crisp, turning occasionally, about 2 minutes. Drain on paper towels.
Add the cheese to the soup and stir over medium-low heat until melted. Puree in a blender in batches until smooth; season with salt and pepper. Garnish with the prosciutto, more cheese and chives, if using. Serve with bread, if desired.
Photograph by Antonis Achilleos
When blending hot liquid, first let it cool for five minutes or so, then transfer it to a blender, filling only halfway. Put the lid on, leaving one corner open. Cover the lid with a kitchen towel to catch splatters, and pulse until smooth.