Step 1

Preheat oven to 375°F. Butter a 3-quart broiler-safe baking dish. Roast sweet potatoes on a baking sheet until tender, 60 to 70 minutes. Cut a slit in the top to release steam and let cool for 15 minutes.

Step 2

Scoop out sweet potato flesh (discard skins). Transfer to a food processor and process until completely smooth, 30 seconds. Add butter, brown sugar, nutmeg, cayenne pepper, whole eggs, and 1 teaspoon vanilla. Pulse until fully incorporated, 3 to 4 times. Season with salt and black pepper; transfer to the prepared dish.

Step 3

Bake until sweet potatoes are set, 20 to 25 minutes. Let stand for at least 10 minutes.

Step 4

Whisk together egg whites, granulated sugar, and cream of tartar in a bowl. Set the bowl over (but not in) a saucepan of simmering water and cook, whisking constantly, until sugar is dissolved and whites are very warm to the touch, 3 to 4 minutes; remove from heat. Beat with an electric mixer on low speed, gradually increasing speed to high, until glossy and soft peaks form, 4 to 6 minutes. Beat in the remaining 1/2 teaspoon vanilla.

Step 5

Heat the broiler with rack in the middle position. Spoon meringue over cooled sweet potatoes. Broil until meringue is browned, 30 seconds to 1 minute.