Fill a large saucepan or Dutch oven with 1 inch water and bring to a simmer for Step 3. Place a small mixing bowl in the freezer to chill.

Whisk whole eggs and 1/4 cup sugar in a heavy, medium, nonreactive saucepan until smooth. Whisk in espresso (or coffee). Cook over low heat, whisking constantly, until slightly thickened and an instant-read thermometer registers 160 degrees F, about 10 minutes. (Do not let the mixture come to a simmer.) Remove from the heat and whisk in liqueur and vanilla. Transfer to a large bowl and let cool to room temperature, about 20 minutes.

Combine reconstituted egg whites, cold water, cream of tartar and remaining 1/3 cup sugar in a large heatproof mixing bowl. Set the bowl over (not in) the barely simmering water and beat with a hand-held electric mixer at low speed for 4 to 5 minutes. Increase mixer speed to high and continue beating for 3 minutes more. The meringue should hold firm peaks. Remove from the heat and continue beating until cool and fluffy, 3 to 4 minutes.

Whip cream in the chilled mixing bowl (no need to wash meringue from beaters) until soft peaks form.

Whisk one-fourth of the meringue into the cooled coffee mixture. Using the whisk, fold in remaining meringue. With a rubber spatula, fold in whipped cream.

Divide the mixture among six 3/4-cup metal molds (see Tip) or spoon into an 8-by-4-inch metal loaf pan. Cover with plastic wrap and freeze until firm, at least 6 hours.

Before serving, toast hazelnuts at 350 degrees F until fragrant, about 5 minutes. (Alternatively, microwave hazelnuts on high for 4 minutes, stirring twice.) Let cool. Dip bottoms of molds or pan in hot water for a few seconds, then invert onto chilled dessert plates or a serving platter. Garnish with hazelnuts and serve.