Turn the cauliflower upside down on a cutting board. Cut off and discard most but not all of the stems, then cut the florets into small, 1/2-inch clusters. Place the florets on a sheet pan, toss them with the olive oil, red pepper flakes, 1 teaspoon salt, and 1/2 teaspoon black pepper, and spread them out in a single layer. Roast for 25 to 30 minutes, tossing two or three times, until the florets are tender and randomly browned. Set aside to cool for 10 minutes.
Set the oven to broil and arrange a rack 6 inches below the heat.
Transfer the florets to a large mixing bowl and add the mascarpone, stirring to coat the florets evenly. Stir in the Gruyere, prosciutto, nutmeg, 1 teaspoon salt, and 1/2 teaspoon black pepper.
Toast the bread in a toaster until lightly browned, and place in a single layer on a sheet pan lined with foil. Mound the cauliflower mixture evenly on each toast and dust with paprika. Broil the toasts for 2 to 4 minutes, until browned and bubbling. (Watch them carefully!) Transfer to plates and sprinkle with Parmesan, the chives, and sea salt. Serve hot.