1 1/4 cups sugar
1 1/2 cups unsalted butter, room temperature, cut into tablespoons
1 teaspoon pure vanilla extract
1 1/2 cups (12 ounces) strawberry jam, pureed in a food processor
In the heatproof bowl of an electric mixer set over a saucepan of simmering water, combine egg whites and sugar. Cook, whisking constantly, until sugar has dissolved and mixture is warm to the touch (about 160 degrees).
Attach the bowl to the mixer fitted with the whisk attachment. Beat the egg-white mixture on high speed until it holds stiff (but not dry) peaks. Continue beating until the mixture is fluffy and cooled, about 6 minutes.
Switch to the paddle attachment. With mixer on medium-low speed, add butter several tablespoons at a time, beating well after each addition. (If frosting appears to separate after all the butter has been added, beat on medium-high speed until smooth again, 3 to 5 minutes more.) Beat in vanilla. Beat on lowest speed to eliminate any air bubbles, about 2 minutes. Stir in strawberry jam with a rubber spatula until frosting is smooth.