Melt butter in a small saucepan over medium heat, stirring frequently, until golden brown. It will develop brown flecks and a nutty fragrance. (About 6-8 minutes.)
Add the dark corn syrup and sugar, cooking for an additional 1-2 minutes, or until the sugar is dissolved.
Remove from heat and cool for 10-15 minutes, or until the mixture is close to room temperature.
Whisk in the eggs, bourbon, and vanilla.
Fold in the pecan halves.
Pour the mixture into the unbaked pie shell.
Bake at 350 degrees for 40-45 minutes, or until the center of the pie puffs, and the filling is set.
Transfer to a wire rack to cool completely. It helps to chill the pie in the refrigerator for 1-2 hours before cutting. Even if you serve the pie at room temperature, an hour or so in the fridge helps it to firm up.