Combine the raspberries and 2/3 cup sugar in a blender and process until fully smooth. Pour through a fine-mesh sieve set over a bowl, pressing the solids gently to extract all liquid while discarding the seeds. Mix in the raspberry liqueur and leave at room temperature while you prepare the other components.

Bring a small pot of water to a rolling boil. Add the pistachios and boil for exactly 2 minutes, then drain and plunge them into an ice bath until completely cool. Dry the nuts thoroughly and use your fingers or a clean towel to rub away all the papery skins.

Place the skinned pistachios in a food processor along with 1/3 cup sugar and the fine sea salt. Process continuously for 5 to 8 minutes, stopping to scrape down the sides as needed, until the mixture becomes a smooth, creamy paste as the nuts release their natural oils.

Using an electric mixer in a spotlessly clean, grease-free bowl, beat the egg whites on medium-high speed until they become foamy. Gradually stream in 1/2 cup sugar while continuing to beat, and whip until soft peaks form—the tips should gently fold over when the beaters are lifted. In another bowl, whip the cold cream with 1/3 cup sugar and the vanilla extract until soft peaks form, taking care not to overbeat.

Prepare a loaf pan by lining it with parchment paper, leaving enough overhang on the sides to use as handles later. Add the whipped egg whites to the whipped cream in two separate additions, folding gently with a spatula to maintain the airy texture. Once combined, fold in the pistachio paste just until streaks remain visible throughout—do not fully incorporate.

Spoon one-third of the cream mixture into the lined loaf pan and spread it evenly. Drizzle one-third of the raspberry purée over the cream layer. Repeat this layering process once more with another third of the cream and another third of the purée. Top with the final third of the cream mixture and smooth the surface gently. Cover tightly with plastic wrap or foil and freeze for a minimum of 6 hours, or ideally overnight, until completely firm.

Remove the semifreddo from the freezer and allow it to rest at room temperature for 2 to 3 minutes to soften slightly. Grasp the parchment overhang and lift the entire loaf from the pan, then peel away the parchment. Transfer to a chilled serving platter or cutting board. Drizzle or spoon the reserved raspberry purée over the top and garnish with any extra pistachio pieces or fresh raspberries if desired.

For clean slices, dip a sharp knife into hot water, wipe it dry, and make one smooth cut. Repeat the dipping and wiping between each slice. Serve immediately while still frozen.