Make the cake: Preheat oven to 325 degrees. Generously butter the sides of an 8-inch cake pan and line the bottom with parchment.
Place butter and chocolate in a large heatproof bowl and microwave in 30-second increments, stirring after each, until completely melted; let cool. Whisk in egg yolks and half of the sugar.
Beat egg whites and remaining sugar by hand until glossy, stiff peaks form. Gently fold into chocolate mixture.
Pour batter into prepared pan and bake for 15 to 20 minutes or until cake is set and a toothpick inserted into the center comes out clean. Let cool to room temperature and place in refrigerator for 15 minutes. To unmold, run a knife around the edge of pan to loosen.
Make the raspberry mousse: Place lemon juice in a small bowl and sprinkle with gelatin. Let sit until gelatin softens, 3 minutes. In a blender, puree 2 cups raspberries until smooth, scraping down bowl as needed. Pour through a fine-mesh sieve into a measuring cup, pressing on solids (you should have about 1 cup of puree); discard solids.
In a small saucepan, combine raspberry puree and 1/2 cup sugar over medium. Cook until bubbles form at edge. Add gelatin mixture and cook, stirring constantly, just until gelatin dissolves, about 1 minute. Transfer mixture to a small bowl and let cool to room temperature, 20 minutes. In a large bowl, using an electric mixer, beat cream and 2 tablespoons sugar on medium-high until firm peaks form, about 4 minutes. With a rubber spatula, gently fold in raspberry puree mixture until combined.
Make the chocolate mousse: Put 1 2/3 cups cream into the bowl of an electric mixer fitted with the whisk attachment; beat on medium-high speed until soft peaks form, about 3 1/2 minutes. Transfer to a bowl; refrigerate 1 hour.
Put 4 egg yolks into the clean bowl of the mixer fitted with the clean whisk attachment; beat on high speed until pale and frothy, 4 to 5 minutes. Meanwhile, bring 1/4 cup sugar, 2 tablespoons corn syrup, and 2 tablespoons water to a rolling boil in a small, heavy saucepan over high heat. Cook until clear, large bubbles form, about 1 minute. Reduce mixer speed to medium-low. Carefully pour hot syrup down side of bowl. Raise speed to medium-high. Mix until slightly thickened, about 5 minutes. Using a rubber spatula, stir in bittersweet chocolate, 1 teaspoon vanilla, and a pinch of salt.
Add one-third of bittersweet-chocolate mixture to whipped cream; whisk to combine. Add remaining bittersweet-chocolate mixture, whisking until completely combined. Press through a large-mesh sieve into a large bowl; discard any solids.
Make the ganache: Place chocolate in a large heatproof bowl and set aside. In a small saucepan, bring cream to just a boil. Remove cream from heat and pour over chocolate. Let stand, without stirring, for 30 seconds. Whisk until smooth. Set aside at room temperature until cool and spreadable.
Assemble the semifreddo: Trim cake to 1 inch high. Place cake in the bottom of a 3-inch-tall cake ring.
Transfer raspberry mousse into a pastry bag fitted with a large round tip (such as Ateco #808). Pipe a 1 inch layer of raspberry mousse on top of the chocolate cake. Freeze until mousse begins to set, 30 minutes. Repeat with chocolate mousse and freeze for 30 minutes.
Spread a thin layer of chocolate ganache on top of the chocolate mousse and freeze 10 minutes until set.
Remove the cake ring either by warming the outside of the cake with a heat gun (recommended) or allowing the cake to warm slightly on its own (which will result in a messier exterior). Freeze for at least 1 hour or up to 3 days.
Before serving let cake warm for 30 minutes and garnish with candies hazelnuts.