Step 1

Position a rack in middle of oven; preheat to 350°. Line two 8"-diameter cake pans with parchment paper rounds (do not grease). Beat egg whites, salt, cream of tartar, and ½ cup (100 g) sugar in the bowl of a stand mixer fitted with the whisk attachment on medium-low speed until egg whites are broken up, about 30 seconds. Increase speed to medium-high and beat until meringue is glossy and holds firm peaks, 8–10 minutes.

Step 2

Whisk egg yolks and remaining ½ cup (100 g) sugar by hand in a large bowl until pale and well combined, about 2 minutes. Whisk in oil, vanilla, and ⅓ cup room-temperature water. Sift flour and baking powder over and whisk vigorously to combine.

Step 3

Add one fourth of meringue to egg yolk mixture and mix thoroughly to incorporate (this will lighten the batter). Add remaining meringue in 3 batches, gently folding after each addition until only a few streaks of meringue remain (err on the side of mixing slightly less rather than more to keep batter billowy).

Step 4

Divide batter evenly between prepared pans and gently smooth surface. Bake cakes 15 minutes. Reduce oven temperature to 325° and continue baking until golden brown and tops spring back when gently pressed, 35–40 minutes more. Remove from oven; invert pans onto a wire rack. Let cakes cool in pans (cooling them upside down reduces shrinkage), 60–70 minutes. Turn cakes over and run an offset spatula around sides of cakes to loosen, then invert cakes onto wire rack. Peel away parchment.

Step 5

Finely grind sugar and 1½ cups (37 g) freeze-dried raspberries in a spice mill or food processor (if using food processor, sift powder through a fine-mesh sieve after to remove seeds). Transfer to the clean bowl of a stand mixer fitted with the whisk attachment; add cream, vanilla, and salt and beat on medium-high speed until firm peaks form, 5–7 minutes.

Step 6

Stir jam in a small bowl to loosen, then gently fold in fresh raspberries.

Step 7

Place 1 cake on a cake platter or large plate. Scoop a heaping cupful of raspberry cream on top; spread evenly with offset spatula. Spoon berry mixture on top of cream, leaving a 1" border around the edges (this will prevent berries from spilling over the sides). Place second cake layer on top. Spoon a heaping ½ cup raspberry cream into pastry bag fitted with tip. Frost top and sides of cake with raspberry cream still in bowl, then pipe dollops of raspberry cream around edges of top of cake. Chill cake, uncovered, at least 2 hours.

Step 8

To serve, sprinkle top of cake with crushed freeze-dried raspberries if desired. Slice cake with a serrated knife, wiping clean between cuts.Do ahead: Cake can be baked 1 day ahead; store tightly wrapped at room temperature, or freeze up to 1 week. If frozen, thaw in refrigerator overnight before using. Cake (without crushed raspberry topping) can be assembled 1 day ahead; cover loosely and chill.