In a food processor, combine the flour, salt, and 1 tablespoon of the sugar. Add the butter and pulse until the mixture resembles a coarse meal. Add cold water, 1 tablespoon at a time, and pulse until the dough comes together but is still slightly crumbly (approx. 3 to 4 Tbsp total). Turn dough out onto a lightly floured surface and knead for a couple of minutes. Shape the dough into 2 disks, wrap in plastic wrap, and refrigerate for 20 minutes.

On a  clean, lightly floured work surface, roll out 1 disk of the dough until it is 1/4" thick. Using a small pot lid or plate with a 6" inch base, cut out as many rounds as you can. Repeat this process with the second disk of dough. Reroll the scraps if you have to, making sure you have 8 rounds of dough. Transfer to parchment paper–lined baking sheets and refrigerate 20 minutes.

Preheat oven to 375 degrees. On a rimmed baking sheet, spread out the pecans and toast for about 8 minutes. Cool and then coarsely chop.

In a medium saucepan over medium heat, combine 1 cup of sugar with 1/2 cup of water. Swirl the pan gently once the caramel begins to form until the mixture is a medium color, approximately 9 minutes. Remove from heat. Whisk in butter, cream, 1 tsp vanilla and salt.

Transfer 1 cup of the caramel to a large bowl to cool slightly. Whisk in remaining cup of sugar and 1 tsp vanilla extract and corn syrup. Whisk in the 4 unbeaten eggs until smooth. Stir in pecans.

Grease a 9x13" baking pan. Pour pecan filling into the pan and bake for 30 minutes. Scrape out into a bowl and stir gently to combine. Refrigerate until chilled, approximately 1 hour.

Brush the pastry rounds with some of the beaten egg. Add 1/4 cup of the pecan filling onto each round and fold pastry over to create a hand pie. Press edges to seal and crimp closed with a fork. Repeat with the remaining dough rounds.

Brush tops of the pies with beaten egg and sprinkle with sugar. Make 2 slits in the top of each pie. Bake for 40 minutes, until golden brown. Cool before serving.