Heat oven to 400°F. In a bowl, whisk eggs; set aside. In another bowl, combine chocolate, butter and vanilla. In a heavy-bottomed pot (to prevent burning), combine milk with 1/2 cup sugar and salt over medium heat; whisk constantly until mixture comes to a simmer.
Remove pot from heat.
Whisk milk mixture into eggs until combined.
Whisk chocolate-butter mixture into milk-egg mixture; spoon custardinto piecrust.
Bake pie until it begins to set at edges but center jiggles slightly when you shake pan, 13 to 15 minutes.
Remove pie from oven; let cool for at least 3 hours.In a bowl, 10 minutes prior to serving, toss apricots with remaining 1 tablespoon sugar; arrange apricots on top of pie.
