Thaw pie crust, then pierce with a fork. Foil and add pie weights and bake for 15 minutes. Allow to cool.
In a small saucepan, bring the cream, vanilla, and 1/3 cup of sugar to a simmer over medium heat. Let cool to room temperature.
In a medium bowl, whisk the egg yolks and remaining 1/3 cup sugar together.
Pour the cream into the yolks in a steady stream, whisking constantly to combine.
Bake at 325 F until the custard is set around the edges, but still noticeably jiggly in the center, 25 to 30 minutes. Cool to room temperature.
When the pie is cool, sprinkle 2 tablespoons sugar in an even layer over the pie. Brûlée the sugar in the broiler until evenly melted and caramelized. Let sit at least 5 minutes before serving.
