In a small pot, brown the butter by melting it over medium-high heat, stirring vigorously until browned. This should take 4-6 minutes. Then, let it cool.
In a medium bowl, add the sugar and eggs. Mix until combined using a hand mixer.
Add the Karo syrup and vanilla extract to the mixture. Mix by hand using a rubber spatula until well combined.
Stir in the pecans with the spatula.
Add the browned butter to the mixture and mix again with the spatula until thoroughly combined.
Pour the mixture into the frozen pre-made pie crust. If desired, add a layer of halved pecans on top for decoration.
Bake in the oven for 45-50 minutes, or until the middle slightly jiggles while the edges remain firm.
If the pie crust edge is getting too brown, cover the edges with aluminum foil.
Cool for 30 minutes or refrigerate for 2 hours until chilled before serving.
Notes
Halfway through baking, rotate the pan to ensure that the pie cooks evenly on all sides.
If you are choosing to use pecan halves, arrange them on the surface of the pie in a decorative pattern. You can do this halfway through the baking of the pie or before you place the pie in the oven. Don't worry about the pecan halves sinking, they will rise to the top as the pie bakes.