Baked-Alaska Tree

Open a standard manila file folder. Roll it into a cone with an 8-inch diameter; tape to seal. Cut off excess to make a flat base with a 7 1/2-inch diameter. Roll a similar-size piece of parchment; fit inside cone. Place cone in a pot, tip down (to hold it upright). Pulse wafers in a food processor with 1/3 cup sugar; add butter and salt and pulse to moisten crumbs.

Spread chocolate ice cream into cone in a 1-inch-thick layer (leaving center hollow). Freeze 15 minutes. Fill with peppermint ice cream. Pat 1 1/2 cups crumbs evenly on top. Freeze upright, point-down in pot, at least 8 hours and up to 3 days. Invert on a serving plate; remove mold and parchment. Let stand until slightly softened, 5 minutes. Pat remaining crumbs over outside of cone. Return to freezer.

Whisk egg whites and remaining 1 cup sugar in the heatproof bowl of a stand mixer and place over a pot of simmering water. Whisk constantly until sugar dissolves and egg whites are warm to the touch, about 3 1/2 minutes. Place bowl in stand mixer fitted with whisk attachment and whip, starting on low speed and gradually increasing to medium-high, until egg whites are foamy. Add cream of tartar and continue to whip until stiff, glossy peaks form. Fold in cornstarch and vanilla. Transfer to a pastry bag fitted with a large round tip (such as Ateco #806)

Starting at bottom of tree, and holding tip perpendicular to it, pipe upward, dragging meringue into teardrop shapes for a snowy effect. Lightly brown meringue with a kitchen torch. To serve, cut a piece from tip to base, then slice crosswise. (Cake can be made up to 3 days ahead; freeze it whole before piping on meringue.)