Pulse flour, sugar, and salt in a food processor.

Add shortening and pulse until combined.

Add cold butter and pulse until the mixture resembles coarse meal.

Whisk egg and ice water, then add to the processor and pulse briefly.

Turn the dough onto plastic wrap and flatten into a disk.

Wrap and chill for at least 1 hour.

Roll the dough into a 12-inch round on a floured surface.

Place the dough in a 9-inch pie plate and crimp the edges.

Chill for 30 minutes.

Preheat oven to 450°F (232°C) with a baking sheet on the lower rack.

Scrape vanilla seeds into a skillet, add butter and the vanilla pod.

Cook over medium-high heat until butter browns.

Remove from heat.

Whisk eggs, corn syrup, sugar, vinegar, and salt in a bowl.

Gradually whisk in the browned butter mixture and discard vanilla pod.

Add vanilla extract if not using vanilla bean.

Spread chopped pecans in the crust.

Pour in the corn syrup mixture.

Top with pecan halves.

Place pie on the hot baking sheet, reduce oven temperature to 350°F (175°C) and bake for 20-30 minutes.

Cover the top with foil and continue baking until set, 25-30 minutes.

Remove foil.

Cool completely on a rack.