Make the Garnish: Preheat the oven to 175 degrees F.
Arrange the prosciutto on a parchment-paper-lined baking sheet and bake until dried and crispy, about 3 hours. Set aside. (The prosciutto can be made up to 2 days in advance, and kept covered in an air-tight container.)
When the prosciutto is done, combine the squash, water, 1 teaspoon butter, salt, and sugar in a large skillet over medium-high heat. Cook, stirring occasionally, until the liquid has evaporated and the squash is tender and glazed.
Make the Nage: Combine all the ingredients, except the water, in a pot and bring to a boil. Lower the heat and simmer for 45 minutes. Strain, discard the solids, and return to the pot. Boil until reduced to 3 cups. Set aside. (The nage can be made up to 3 days in advance and refrigerated, covered.)
Make the Scallops and Orange Vapor: Using a vegetable peeler, peel the rind off the oranges and set aside. Reserve orange segments for another use.
Preheat a large skillet over high heat. Season the scallops with salt and pepper, to taste. Add the oil and heat. Add the scallops and cook, turning once, until seared and just cooked through, about 3 minutes per side.
Meanwhile, heat the nage in a saucepan over medium heat. While blending with an immersion blender, add the butter to the nage, little by little, to make frothy.
Heat the remaining 1 teaspoon butter in a medium skillet over medium heat. Add the glazed butternut squash and reheat.
Bring a teapot of water to a boil.
Divide the glazed butternut squash among the center of 8 small bowls, and top each with a scallop. Spoon some of the frothy nage over each scallop and top each with piece of the crispy prosciutto. Place each bowl inside a heated larger bowl and surround with the orange rind.
Place the bowls in front of your eagerly awaiting guest. Pour the water from the teapot over the orange rind to create orange vapor. Inhale the vapor while you eat.