Step 1: Prepare the Pie Crust: In a large bowl, whisk together flour and salt. Cut in the cold butter using a pastry blender or your fingertips until the mixture resembles coarse meal with some pea-sized butter chunks. Gradually add ice water, 1 tablespoon at a time, mixing until the dough just comes together. Do not overmix. Form into a disc, wrap in plastic wrap, and refrigerate for at least 30 minutes.
Step 2: Preheat Oven & Roll Crust: Preheat your oven to 375°F (190°C). On a lightly floured surface, roll out the chilled pie dough into a 12-inch circle. Carefully transfer it to a 9-inch pie plate. Trim and crimp the edges as desired. If using store-bought, prepare as directed.
Step 3: Toast Pecans: Spread pecan halves on a baking sheet and toast in the preheated oven for 5-7 minutes, or until fragrant. Let cool slightly. Reduce oven temperature to 350°F (175°C).
Step 4: Prepare the Caramel Base: In a medium saucepan, melt 1/2 cup butter over medium heat. Add granulated sugar and brown sugar, stirring until dissolved. Stir in the heavy cream, corn syrup, and 1/4 teaspoon salt. Bring to a gentle simmer, then reduce heat to low and cook for 5 minutes, stirring occasionally. Remove from heat and stir in the vanilla extract. Let cool for 10 minutes.
Step 5: Combine Filling: In a separate bowl, lightly beat the 2 large eggs. Gradually whisk a small amount of the cooled caramel mixture into the beaten eggs (temper the eggs) to prevent scrambling. Then, slowly pour the egg mixture back into the remaining caramel mixture, whisking constantly until fully combined.
Step 6: Assemble the Pie: Sprinkle the toasted pecan halves evenly over the bottom of the prepared pie crust. Pour the caramel filling over the pecans.
Step 7: Bake the Pie: Bake at 350°F (175°C) for 50-60 minutes, or until the edges are set and slightly puffed, but the center still has a slight jiggle. If the crust edges brown too quickly, cover loosely with foil.
Step 8: Cool Completely: Remove the pie from the oven and place it on a wire rack. Allow it to cool completely for at least 4-6 hours, or preferably overnight, before slicing and serving. This is crucial for the filling to set properly.