Make the filling: In a saucepan, combine apples, brown sugar, lemon or apple juice, vanilla, and cinnamon. Cook over medium heat for 8–10 minutes until the apples are soft. In a small bowl, stir together 2 tablespoons of cornstarch with ½ cup of water. Add to the pan and cook for 1–2 more minutes, until the mixture thickens. Remove from heat and let cool completely.
Make the dough: In a large bowl, mix flour, sugar, and salt. Cut in butter until crumbly. Stir in a mixture of 1 egg and buttermilk. Form into a dough ball, wrap in plastic, and chill 1 hour.
Roll and shape: Divide chilled dough into 8 pieces (about 155–160g each). Roll into balls, then flatten each into a 6-inch circle. Fill one half with 2 tablespoons of filling. Brush edges with beaten egg, fold, and crimp shut. Cut a slit in the top.
Fry: Heat oil in a deep pan to 350°F. Fry pies 2–3 minutes per side, turning as needed. Drain on paper towels.
Glaze: In a small bowl, whisk together powdered sugar, milk or cream, and vanilla extract (if using) until smooth and pourable. Brush over warm pies or dip the tops. Let rest for 10–15 minutes until set.
Want to take it to the next level? Try these with my Maple Glaze Recipe for the ultimate cozy fall treat.