Make the fudge sauce: Combine the heavy cream, brown sugar, corn syrup, butter and salt in a medium saucepan; bring to a simmer over medium heat, stirring occasionally. Add the chocolate and cocoa powder and continue to cook, stirring constantly, until smooth, thick and glossy, 1 to 2 minutes. Let cool.
Make the ice cream cake: Coat a 3 1/2-quart metal or glass bowl with cooking spray and line with plastic wrap, leaving a 1-inch overhang. Scoop one kind of ice cream into the bowl and spread in an even layer. Top with a second kind of ice cream and then a third. Use a piece of plastic wrap to pack in the ice cream evenly. Drizzle with half the fudge sauce and arrange half the pound cake slices in a single layer over the top. Cover with plastic wrap and freeze until set, about 30 minutes.
Uncover the ice cream cake and spread the fourth kind of ice cream on top; repeat with the fifth kind of ice cream. Use a piece of plastic wrap to pack it in. Drizzle with the remaining fudge sauce and cover with the remaining pound cake slices in a single layer. Cover with plastic wrap and freeze until firm, at least 4 hours or overnight.
Make the meringue: Stir the granulated sugar and cocoa powder in a small bowl. Beat the egg whites and cream of tartar in a large bowl with a mixer on medium-high speed until foamy, 30 seconds to 1 minute. Gradually beat in the sugar-cocoa mixture. Increase the mixer speed to high; beat until the sugar is dissolved and stiff peaks form, 4 to 5 minutes.
Uncover the ice cream cake and invert onto a foil-lined baking sheet. Let stand until the cake slips out of the pan easily, then remove the plastic wrap. Spread the meringue over the top and sides of the cake, making the top slightly thicker. Make swirly peaks in the meringue using the back of a spoon. Freeze until firm, at least 3 hours or up to 2 days.
Brown the meringue with a kitchen torch (or bake at 500˚ until golden, 3 to 5 minutes). Use 2 large spatulas to transfer the baked Alaska to a platter and slice into wedges.