Preheat the oven to 350°. On a baking sheet, toss a handful of the kale with 1 tbsp. oil. Bake, turning once, until crisp, 7 to 8 minutes.
In a dry skillet, cook the prosciutto over medium-high heat until crisp, 2 to 3 minutes. Transfer to paper towels; let cool. Crumble.
In a large pot with a lid, heat the remaining 2 tbsp. oil over medium-high. Add the remaining kale, the leek, and coriander; season with salt and pepper. Cook, stirring often, until the kale wilts, about 5 minutes. Add the stock and beans. Cover partially and cook, stirring often, until the vegetables are tender, 15 to 20 minutes. Stir in the spinach and 1/2 cup cream. Puree the soup; season.
Divide the soup among bowls. Drizzle with cream. Top with the kale chips and crispy prosciutto.
