Line a standard 5-by-9-inch loaf pan with plastic wrap, leaving a 2-inch overhang on all sides. Pulse pistachios in a food processor until coarsely chopped (some will break down to a coarse grind). Transfer to a small bowl; do not wipe processor clean. Place strawberries and 3 tablespoons sugar in processor; puree until smooth and transfer to a fine sieve set over a bowl. Stir puree, pressing on solids to extract as much liquid as possible; discard solids.

Combine egg yolks and remaining 1/2 cup sugar in a bowl set over a pot of simmering water. Beat on high speed (or vigorously by hand) until pale yellow and tripled in volume, about 3 minutes. Transfer bowl to a larger bowl of ice water; stir until mixture is very thick and cool, about 3 minutes.

Beat together cream and vanilla in a large bowl until soft peaks form. Whisk 1/3 of whipped cream into egg mixture, whisking until smooth, then fold into remaining cream with a rubber spatula just until thoroughly incorporated.

Pour 1/2 of cream mixture into strawberry puree. Gently fold together until thoroughly incorporated, then pour into loaf pan and smooth top. Fold pistachios into remaining cream mixture and pour evenly over strawberry cream; smooth top. Fold plastic wrap over surface and freeze at least 12 hours and up to 3 days. To serve, peel plastic from surface. Invert pan onto a cutting board. Unmold semifreddo, remove plastic, and cut crosswise into 3/4-inch-thick slices.