Mix 2 tablespoons of the syrup with the cornstarch and stir until completely smooth and no lumps remain. Add eggs to the bowl of a stand mixer and mix. Add the syrup-cornstarch mixture to the eggs, along with the remaining syrup, caramel, and vanilla. While continuing to mix on low speed, slowly add melted butter. Beat on low for 2 minutes until mixture is smooth and slightly bubbly. Remove bowl from mixer and stir pecan halves in by hand. Pour mixture into pie crust and bake for 30 minutes.