In a small pan, whisk the sugar and eggs over medium heat, whisking constantly until the mixture reaches 160 degrees F, about 2-4 minutes. You can test it with a thermometer; however, I always double check by dipping a spoon in the mixture, then swiping a finger down the middle. The mixture should be thick enough to maintain the line you swiped, not dripping into it.
1 ⅓ cups granulated sugar, 4 eggs
Remove from the heat and immediately add the chopped chocolate and vanilla. Whisk until the chocolate is melted and the mixture is completely smooth, then set aside to cool, stirring occasionally, until it is just warm so that it doesn't melt the butter in the next step (about 120-124 degrees F, which took about 8-10 minutes in my cool kitchen). I find it best to pour the mixture into a separate bowl to help it cool more effectively.
8 oz dark or bittersweet chocolate, 2 teaspoon vanilla
Meanwhile, in a stand mixer with a paddle attachment or large bowl with hand beaters, beat the butter on medium speed for 2-3 minutes, until it is light and fluffy. While the mixer is still going, slowly add the cooled chocolate mixture. Scrape the bowl halfway through. Once all the chocolate is added, increase to high speed and beat for 5 minutes, until it is fluffy and lighter in color.
10 tablespoon butter
In a separate clean bowl, beat the whipped cream and powdered sugar with the whisk attachment on high speed until stiff peaks form, about 7 minutes in my mixer. This really depends on your mixer; the goal is get it to stiff peaks, but avoid over beating it or the texture becomes clumpy/curdled looking.
1 ⅓ cups heavy cream, 2 tablespoon powdered sugar
Fold the whipped cream into the chocolate mixture with a rubber spatula until it is evenly combined and no white streaks remain. I find that turning the bowl in quarter turns as I fold helps the mixture combine more easily.
Pour the filling into the cooled crust and smooth out the top. Cover with plastic wrap and chill in the fridge for at least 6 hours or overnight.