Heat milk, egg yolks, 1/4 cup sugar, gelatin, instant coffee, and salt over medium heat, stirring constantly, until gelatin dissolves, about 5 minutes. Remove from heat and stir in vanilla extract. Chill until gelatin mixture is thickened to the consistency of unbeaten egg whites, about 1 hour.
Beat egg whites in a glass or metal bowl until foamy. Gradually add 1/4 cup sugar, continuing to beat until soft peaks form. Lift your beater or whisk straight up: the egg whites will form soft mounds. Fold gelatin mixture into egg whites.
Beat heavy cream in another until stiff peaks form. Fold egg white-gelatin mixture into whipped cream until evenly blended.
Line a loaf pan with waxed paper.
Spread about 1/4 the cream mixture into prepared loaf pan. Layer about 7 wafers over cream mixture. Repeat layers, ending with the cream mixture. Cover and refrigerate until set, about 3 hours.
If you leave the gelatin mixture too long (as I frequently do) and it sets, you can melt it over low heat on the stove top.