Place flour, sugar, salt, vinegar, and egg yolk in the bowl of a food processor and pulse lightly 1 time. While pulsing, add butter gradually; dough should be the consistency of cornmeal. Do not over-mix or dough will become tough and hard to roll out. While pulsing, add ice water slowly until dough forms a ball (again being careful to not over-mix). Turn off processor as soon as dough forms a ball and refrigerate dough for about 30 minutes.
Combine apricots, jam, nectar, sugar, and pumpkin pie spice in a medium saucepan and bring to a simmer over medium heat, stirring frequently, for 10 to 15 minutes. Add cornstarch slurry and continue simmering for another 5 minutes. Remove from heat and add almond and vanilla extracts. Let cool to room temperature; mixture should thicken to the consistency of a jam.
Meanwhile, pour several inches of oil into a large, deep, heavy-bottomed pan or Dutch oven; oil should not come more than halfway up the sides of the pan. Heat oil to 360 degrees F.
On a floured board, roll out dough to 1/8-inch or less thickness. Cut or stamp dough into 15 (6-inch) round circles, or as many that size as possible. Spoon about 2 tablespoons of filling into the center of each circle of dough and brush edges with egg wash. Fold in half and press edges together with a fork dipped in flour. Poke the top of the crust twice with fork.
Carefully add pie pockets, in batches, to the hot oil and deep fry until golden brown, turning as needed. Remove from oil and drain on paper towels. Sprinkle with cinnamon sugar and serve; be careful as filling is hot.
A viewer or guest of the show, who may not be a professional cook, provided this recipe. It has not been tested for home use.