Whisk together egg whites and sugar in the top pan of a double boiler (or, make your own by setting a heatproof bowl on top of a saucepan filled with an inch or two of simmering water—make sure the bottom of the bowl does not touch the water). Cook over medium-high heat, whisking intermittently, until the egg mixture registers 160 (F) on a candy thermometer.
Once hot, immediately pour into the bowl of a stand mixer fitted with the whisk attachment. Beat on high speed for 8 to 10 minutes, until the mixture is light, fluffy, and holds medium-stiff peaks. When done, the outside of the mixer bowl should be at room temperature. Scrape down the bottom and sides of the bowl, and the whisk attachment. Swap the whisk attachment for the paddle attachment.
With the mixer on low, add the butter, a few tablespoons at a time. Once incorporated, increase to medium-high and beat until the buttercream is silky smooth, 3 to 5 minutes. Scrape down the bottom and sides of the bowl. With the mixer on low, gradually add the jelly, 1 to 2 tablespoons at a time. Once incorporated, increase to medium-high and beat until silky smooth and pale pink-purple, 2 to 3 minutes more.