Blend the raspberries with 2/3 cup sugar until completely smooth, then strain through a fine-mesh sieve to remove the seeds, pressing gently on the solids to extract all the liquid. Stir in the raspberry liqueur and set aside at room temperature. This seedless purée will give you a silky texture throughout the dessert.
Bring a small pot of water to a boil and add the pistachios, boiling for 2 minutes. Drain immediately and transfer to an ice bath to cool completely, then pat dry and rub off the papery skins using your fingers or a clean towel. Process the skinned pistachios with 1/3 cup sugar and fine sea salt in a food processor, scraping down the sides frequently, until the mixture transforms into a smooth, creamy paste—this should take 5–8 minutes as the nuts release their oils. I find that grinding pistachios into a paste rather than leaving them chunky creates a more elegant, cohesive texture in the semifreddo.
In a clean, grease-free bowl, beat the egg whites with an electric mixer on medium-high speed until foamy, then gradually add 1/2 cup sugar and continue beating until soft peaks form (the peaks should gently fold over when you lift the beaters). In a separate bowl, whip the cold cream with the remaining 1/3 cup sugar and vanilla extract until soft peaks form as well—don't overbeat or you'll end up with butter. The dual whipping creates two different types of airiness that combine for the semifreddo's characteristic light, mousse-like texture.
Line a loaf pan with parchment paper, allowing some to overhang the sides for easy removal later. Gently fold the egg whites into the whipped cream using a spatula in two additions, being careful not to deflate either mixture. Once combined, fold in the pistachio paste until just streaked through (you want some visual interest, not uniform color). This folding technique preserves all that aerated texture you've worked to build.
Spread 1/3 of the cream mixture from Step 4 into the lined loaf pan, top with 1/3 of the raspberry purée from Step 1, then repeat with another third of each layer. Finish with the final third of the cream mixture on top, smoothing it gently. Cover the pan with plastic wrap or foil and freeze for at least 6 hours, preferably overnight, until completely firm.
Remove the semifreddo from the freezer and let it sit at room temperature for 2–3 minutes to slightly soften the exterior. Using the parchment overhang, carefully pull the semifreddo from the pan and peel away the parchment paper. Place on a chilled serving platter or cutting board, drizzle or spoon the remaining raspberry purée over the top, and scatter over any reserved pistachio pieces and fresh raspberries if desired. Slice with a sharp knife dipped in hot water between each cut for clean, neat slices, and serve immediately.
