Heat 3/4 cup cream in a 1-quart heavy saucepan until hot. Whisk together yolks, sugar, and a pinch of salt in a metal bowl until combined well, then add hot cream in a slow stream, whisking until combined.
Transfer mixture to saucepan and cook over moderately low heat, stirring constantly, until it registers 160°F on thermometer (mixture will be thick).
Pour custard through a fine-mesh sieve into a bowl and stir in vanilla.
Melt chocolate in a double boiler or a metal bowl set over a pan of simmering water stirring frequently. Whisk custard into chocolate until smooth, then cool.
Beat remaining 1 1/4 cups cream in a bowl with an electric mixer until it just holds stiff peaks. Whisk one third of cream into chocolate custard to lighten, then fold in remaining cream gently but thoroughly.
For the Italian Buttercream:
In a small saucepan over medium heat, bring sugar and 1/3 cup water to a boil.
Boil until syrup reaches soft-ball stage (238 degrees.on a candy thermometer). In an electric mixer fitted with the whisk attachment, beat egg whites on low until foamy.
Add cream of tartar; beat on medium high until stiff but not dry.
With mixer running, pour syrup down side of bowl into egg whites in a steady stream, and beat on high speed until steam is no longer visible and bowl begins to feel cool to the touch, about 3-5 minutes.
With the mixer still running, beat in butter a few pieces at a time. Add vanilla and beat until smooth. If it looks curdled at any point, keep beating to smooth out.