In a skillet over medium heat, melt 2 tablespoons of butter. Add the diced apples, then sprinkle with 1/4 cup granulated sugar, 2 tablespoons brown sugar, 1 teaspoon ground cinnamon, 1/4 teaspoon ground nutmeg, and 1 teaspoon lemon juice. Cook for 5-7 minutes, stirring occasionally, until the apples begin to soften.

Whisk together 1 tablespoon cornstarch and 2 tablespoons water in a small bowl until smooth. Pour the slurry into the skillet and continue cooking for another 1-2 minutes until the mixture thickens. Remove from heat and stir in 1 teaspoon vanilla extract. Allow the filling to cool slightly.

For those using refrigerated biscuits, flatten each biscuit into a 5-6 inch circle. If using refrigerated pie crusts, cut out circles of about the same size.

Place about 2 tablespoons of the cooled apple filling in the center of each dough circle. Fold the dough over to create a half-moon shape and press the edges firmly with a fork to seal.

Heat 2-3 cups of vegetable oil in a deep pot until it reaches 350°F. Carefully lower the pies into the hot oil in batches (avoid crowding) and fry for 2-3 minutes per side until they become golden brown and crispy.

Transfer the fried pies to a paper towel-lined plate to drain excess oil. Optionally, dust with powdered sugar, drizzle with caramel sauce, or toss in a cinnamon-sugar mixture while still warm before serving.