Preheat the oven to 350°F (175°C). Roll out the pie crust on a floured surface and fit it into a 9-inch pie dish. Trim excess edges and set aside.
In a mixing bowl, whisk together the granulated sugar, corn syrup, eggs, melted butter, vanilla extract, and sea salt until the mixture is smooth and homogeneous.
Pour the filling mixture into the prepared pie crust, spreading evenly. Sprinkle the pecan halves over the top, pressing down slightly to ensure they are partially submerged.
Bake in the preheated oven for about 50 minutes, or until the filling is set and the pecans are toasted and golden brown. Gently shake the pie; the filling should jiggle slightly at the center but not slosh.
Remove the pie from the oven and allow it to cool completely on a wire rack. The filling will firm up as it cools, achieving a shiny, caramelized top with a crunchy pecan layer.
Slice and serve the pecan pie at room temperature, revealing a smooth, gooey filling contrasted by a toasted nut topping.
