Coat a 9x5" loaf pan with nonstick spray and line with plastic wrap, leaving a generous overhang on all sides.
Combine plums, cardamom, 1/3 cup sugar, and a pinch of salt in a medium saucepan. Cover and cook over medium heat, stirring occasionally, until plums release their juices, about 5 minutes. Uncover and cook until plums soften and start to fall apart, 6-8 minutes longer.
Let cool slightly.
Purée plum mixture in a blender until very smooth. Strain through a fine-mesh sieve into a medium bowl, pressing on solids.
Let cool. Set aside 1 cup purée for serving.
Whisk egg whites, a pinch of salt, and remaining 2/3 cup sugar in a medium heatproof bowl (or the bowl of a stand mixer) and set over a saucepan of simmering water (do not let bowl touch water).
Heat, whisking constantly, until sugar is dissolved and mixture is warm to the touch, about 4 minutes.
Remove bowl from saucepan.
Add vanilla and, using an electric mixer on high speed, beat until mixture is tripled in volume, glossy, and completely cool, about 10 minutes.
Using clean beaters, whip cream in another medium bowl until soft peaks form. Fold 1/3 of whipped cream into eggwhite mixture until just combined. Fold in remaining whipped cream until just combined. Fold in plum purée just until large streaks appear throughout mixture.
Transfer mixture to prepared pan and smooth top. Fold plastic wrap overhang over top and freeze until firm, at least 8 hours.
Unwrap semifreddo and, using plastic overhang, gently lift from pan. Invert semifreddo onto a large platter, remove plastic wrap, and slice 1" thick; transfer to plates and let sit at least 5 minutes to soften slightly.
Serve with reserved plum purée.
DO AHEAD: Plum purée can be made 3 days ahead. Cover and chill. Semifreddo can be made 3 days ahead. Keep frozen.
