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To make soup:.
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1.
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Heat butter and oil in a large, heavy saucepan set over medium heat.
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When hot, add shallots and cook, stirring, until softened and translucent, 3 to 4 minutes or so.
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2.
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Add potatoes and garlic, and cook and stir 1 minute more.
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3.
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Add 2 1/4 cups each of broth and milk, and bring mixture to a simmer.
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Reduce heat and cook at a simmer until potatoes and shallots are tender, about 15 minutes.
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4.
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Gradually whisk in 3/4 cup cheese ad stir until it has melted.
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remove pan from heat and whisk in cayenne pepper.
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Taste and season with salt.
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If you use low-sodium broth, you'll need a teaspoon or more salt.
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If soup is too thick stir in 1/4 each additional broth and milk.
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(Soup can be prepared 1 day ahead; cool, cover and refrigerate.
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Reheat over medium heat, stirring).
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To make garnishes:.
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1.
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Heat 1 tablespoon olive oil until hot in a medium, heavy skillet set over medium heat.
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Add prosciutto and saute, turning often until crisp, 3 to 4 minutes.
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Remove and drain on paper towels.
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2.
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To the same skillet set over medium heat, add 1 tablespoon more olive oil.
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When hot, add bread crumbs and cook, tossing constantly, until golden and crispy, 3 to 4 minutes.
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remove crumbs to a plate.
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(Prosciutto and crumbs can be prepared 4 hours ahead; leave uncovered at cool room temperature).
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3.
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Ladle soup into 4 soup bowls and sprinkle each serving with some parmesan, prosciutto, bread crumbs and parsley.