Directions

1. In a medium bowl, whisk together 1/4 cup sugar, egg yolks, and cornstarch until pale in color; set aside.
2. Combine remaining 1/2 cup sugar, 1/4 cup water, and the vanilla bean and seeds in a medium saucepan. Stir until sugar is completely damp. Heat mixture over high heat until sugar becomes a yellow-golden caramel, about 8 minutes. Remove from heat. Slowly whisk in 1 cup cream, being careful to avoid splatters, then stir in milk.
3. Return caramel mixture to stove and bring to a boil; remove from heat. Pour one third of the caramel mixture into the egg mixture in a slow, steady stream, whisking to combine. Whisk egg mixture into caramel mixture until well combined. Bring to a boil over medium-low heat and cook, whisking constantly, until custard thickens, about 8 minutes. Remove pan from heat; whisk in salt and butter.
4. Strain custard through a fine-mesh sieve into a bowl; pour into prepared pie crust. Transfer pie plate to a wire rack and let filling cool completely. Transfer pie to refrigerator and chill until cold, about 1 hour.
5. Whisk remaining 1 1/2 cups cream until soft peaks form; spread whipped cream over top of pie. Sprinkle brittle over top of pie just before serving. Pie is best eaten day it is made, but can be kept, loosely covered in plastic wrap, refrigerated, up to 2 days.