Preheat the oven to 350°F (175°C). Place the unbaked pie crust into a 9-inch pie dish. Gently press it into the bottom and sides, then crimp the edges as desired.
Add the brown sugar, corn syrup, eggs, melted butter, vanilla extract, salt, and flour to a large mixing bowl. Whisk everything together until the mixture looks smooth and the sugar is mostly dissolved.
Fold the pecan halves into the filling using a spatula. Make sure the pecans are evenly distributed throughout the mixture. Save a few pecan halves if you want to arrange them neatly on top.
Pour the pecan filling into the prepared pie crust. Spread the pecans evenly so every slice gets a good amount. Arrange the reserved pecans on top if desired.
Place the pie dish on a baking sheet and transfer it to the preheated oven. Bake for 50–60 minutes, until the edges are set and the center has a slight jiggle when gently moved. If the crust starts browning too quickly, cover the edges loosely with aluminum foil.
Remove the pie from the oven and place it on a wire rack. Let it cool for at least 2 hours before slicing. The filling will continue to set as the pie cools, giving it that classic gooey texture.
Cut the cooled pecan pie into 8 slices using a sharp knife. Serve at room temperature or slightly chilled with whipped cream or a scoop of vanilla ice cream.