1/2 cup sugar, plus 1 cup

2 1/2 tablespoons water, plus 1/3 cup

2 tablespoons flavored liqueur, such as rum or orange-flavored liqueur

1 quart your favorite flavor ice cream, slightly softened

1/2 quart sorbet or contrasting flavor ice cream, slightly softened

1 (9 by 13-inch) pan brownies

4 egg whites, at room temperature

In a small saucepan combine 1/2 cup sugar and 2 1/2 tablespoons water and bring to a boil. Cook until the sugar is dissolved, then remove from the heat and let cool. When the syrup has cooled to room temperature, add enough of the liqueur to bring the volume up to 1/2 cup. Transfer to an airtight container and refrigerate or place in the freezer until thoroughly chilled.

Lightly butter a 9 by 5 by 3-inch loaf pan and line with parchment paper, leaving a 2 to 3-inch overhanging border on all sides. Using a rubber spatula or the back of a spoon, spread half of the first ice cream into the bottom of the pan, spreading to fill the corners evenly. The ice cream should fill about 1/3 of the pan. Cut a piece of brownie the same size as the pan and press this firmly onto the top of the ice cream. Using a spoon or pastry brush, drizzle half of the chilled syrup over the brownie. Top this with the sorbet or contrasting ice cream flavor, smoothing to fill in the corners of the pan, then follow with the remaining first flavor ice cream, again smoothing to fill in the pan corners. Top with an additional layer of brownie that has been cut to the same size as the pan, and drizzle with the remaining syrup. Fold the overhanging parchment over the top of the cake and wrap the entire cake pan with plastic wrap. Transfer to the freezer for at least 4 hours and up to overnight; it is important that this is frozen solid before proceeding.

Place the egg whites in the bowl of a standing mixer and beat until foamy with slightly soft peaks. Turn off the mixer. Combine the remaining 1 cup sugar and 1/3 cup water in a small heavy saucepan and cook over medium high heat until the syrup registers 250 degrees F on a candy thermometer. Begin beating the egg whites again on medium-high. Slowly drizzle the hot syrup carefully down the side of the bowl, being careful not to pour the hot syrup on the beaters or it will splatter. Continue beating the egg whites until a stiff and a glossy meringue is formed and the outside of the mixing bowl is barely warm, about 5 minutes.

Remove the frozen layered ice cream cake from the freezer and place the cake on a rectangular serving platter that has been lined with aluminum foil. Place the meringue in a pastry bag fitted with a 3/4-inch star tip and decoratively cover the entire cake with the meringue. Transfer to the freezer for 15 minutes.

Remove the cake from the freezer and, using a kitchen torch, brown the meringue lightly all over. Alternately, instead of browning with a torch, preheat oven to 450 degrees F. Freeze desserts for 15 minutes after decorating with the meringue, then bake for 2 to 3 minutes, just until the meringue takes on a bit of color. Remove and serve immediately.