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. Stir in bittersweet chocolate, 1 teaspoon vanilla, and a pinch of salt with a rubber spatula.
Add one-third of bittersweet-chocolate mixture to whipped cream; whisk to combine. Add remaining mixture, whisking until completely combined. Press through a large-mesh sieve into a large bowl; discard any solids. Repeat entire recipe, substituting milk chocolate for the bittersweet.
