In a medium bowl, combine the diced apples with lemon juice, 1/4 cup granulated sugar, cinnamon, nutmeg, and the flour or cornstarch. Toss gently to coat. Set aside.

For the Gooey Caramel Perfection: In a small saucepan over medium heat, melt the butter. Add the brown sugar and a pinch of salt. Stir continuously until the sugar is dissolved and the mixture begins to bubble, about 2 minutes. Pour in the heavy cream and stir well. The mixture will thicken. Continue to cook and stir for another 1 minute, ensuring it is smooth and luscious. Remove from heat. This precise ratio and cooking time for the caramel with the cream is key to its perfect gooey texture later.

Add the prepared apples to the warm caramel sauce, stirring gently to combine.

Preheat your oven to 400 degrees Fahrenheit (200 degrees Celsius). Line a baking sheet with parchment paper.

On a lightly floured surface, roll out one pie crust. Using a 4 to 5 inch round cutter, cut out as many circles as possible. Gather and reroll scraps as needed. Repeat with the second pie crust.

Spoon about 2 tablespoons of the apple caramel filling onto one half of each pie crust circle, leaving a small border around the edge.

Brush the edges of the crust with a little of the beaten egg. Fold the other half of the pie crust over the filling to create a half moon shape. Press the edges firmly to seal, then crimp with a fork.

Place the sealed hand pies on the prepared baking sheet. Brush the tops of the hand pies with the remaining beaten egg and sprinkle generously with extra granulated sugar. Cut a few small slits in the top of each hand pie to allow steam to escape.

Bake for 18 to 22 minutes, or until the crust is golden brown and the filling is bubbling. Let cool on the baking sheet for at least 10 minutes before serving. This cooling time is crucial for the caramel to set into its perfect gooey, flowing consistency.