In a medium bowl, beat egg yolks with 3 tablespoons sugar until foamy and pale. Beat in mascarpone until smooth; set aside.
In the bowl of an electric mixer fitted with the whisk attachment, whisk egg whites until frothy. Add remaining tablespoon of sugar, and beat until they hold stiff peaks. Fold the mascarpone mixture into the egg white mixture. Set aside.
Pour vermouth into a small bowl. Reserve 5 amaretti cookies to crumble and sprinkle over the top of the dessert. One at a time, quickly dip the remaining cookies into vermouth; they should absorb some of the liquid but not be mushy. Place the soaked cookies in a snug layer in the bottom of 8 individual serving bowls or a 9-inch baking dish. Evenly spread half of the mascarpone mixture over the cookies. Repeat layering: Place another layer of soaked cookies over the mascarpone, and then spread remaining mascarpone mixture. End with a layer of soaked cookies that are loosely arranged so that the cream mixture below is visible. Sprinkle with crumbled cookies. Refrigerate to set for at least 2 hours before serving.