The ice cream version of the classic Italian dessert builds on the traditional flavors by using vanilla and coffee ice cream alongside homemade ladyfingers. Martha made this recipe on Martha Bakes episode 604.
Combine 1/4 cup sugar and 2 1/2 tablespoons water in a small saucepan and bring to a boil over medium heat, stirring occasionally. Remove from heat, then stir in espresso and coffee liqueur; let coffee syrup cool. Line a 10-by-5-inch loaf pan with plastic wrap, leaving a 4-inch overhang on both long sides of the pan.
Spread 1/2 vanilla ice cream in bottom of prepared pan. Working quickly, dip 15 ladyfingers, one at a time, in coffee syrup and arrange in a single layer, overlapping slightly, over ice cream. (If ice cream is too soft, return to freezer to firm.) Spread coffee ice cream evenly over ladyfingers. Tap pan against counter to release any air bubbles. Repeat dipping process with remaining 15 ladyfingers and coffee syrup, and arrange on top of coffee ice cream. Spread remaining vanilla ice cream evenly over ladyfingers. Fold over plastic wrap to cover cake. Freeze until firm, at least 5 hours or overnight.
To unmold, let cake stand at room temperature for a few minutes. Unwrap plastic from top and invert cake onto a platter; press a warm damp towel on sides and bottom of loaf pan to release cake, if needed. Remove plastic, then return cake to freezer.
Combine egg whites and remaining 1 1/2 cups sugar in a heatproof standing mixer bowl. Set over (not in) a pan of simmering water, whisking until sugar dissolves and mixture is warm to touch, 3 to 3 1/2 minutes.
Attach bowl to standing mixer fitted with the whisk attachment. Whisk on low speed, gradually increasing speed to high, until stiff, glossy peaks form, about 10 minutes. Add vanilla and cornstarch, and mix meringue until combined.
Remove cake from freezer. Using an offset spatula, spread with meringue, swooping decoratively into peaks, as desired. Hold a small handheld kitchen torch at a 90-degree angle 3 to 4 inches from surface of meringue. Move flame back and forth until meringue is browned and caramelized is spots. Serve immediately.