Add granulated sugar and butter to a small skillet over medium heat. Stir constantly until the sugar has melted and caramelized. Slowly pour, whisking as you do, into the warm cream mixture until well combined.
To prepare the caramel pie filling, add brown sugar, flour, salt, milk, half and half, and egg yolks to a heavy bottomed, 3-4 quart saucepan over medium heat. Whisk together to combine continue to whisk until thick and creamy. Remove from the heat, add vanilla extract.
Preheat oven to 425 degrees. Place pie crust into pie plate and bake for 8 minutes. Remove pie crust from oven and set aside.