In a medium saucepan over low heat, combine 1 1/2 cups water, 3/4 cup sugar, 1/4 cup cornstarch, 1 teaspoon ground cinnamon, and 1 tablespoon lemon juice. Stir constantly and bring the mixture to a boil. Continue stirring for 3-4 minutes until the sauce thickens. Once the sauce has thickened, add the chopped apples and stir. Simmer the mixture for 8-10 minutes, stirring occasionally, until the apples are tender and coated in the thickened sauce.
In a medium bowl, beat the softened cream cheese until it becomes fluffy, which should take about 2-3 minutes. Add 1/3 cup sugar, 1 teaspoon vanilla extract, and 1 tablespoon lemon juice to the cream cheese. Continue beating for another 2 minutes until smooth and creamy. I like to let the cream cheese mixture rest in the fridge for a few minutes before using, so it firms up slightly and is easier to work with.
Place the empanada dough rounds on a clean surface. Add 1 tablespoon of the cream cheese filling (from Step 2) to the center of each dough round, then top with 1 tablespoon of the apple cinnamon mixture (from Step 1). Moisten the edges of the dough with water, fold each round in half, and press the edges together to seal. Use a fork to crimp and seal the edges tightly so the filling doesn’t escape.
Heat the vegetable oil in a cast iron skillet or large frying pan to 375°F (190°C). Working in batches, add a few empanadas at a time, being careful not to overcrowd the pan. Fry the empanadas until they are golden brown on both sides. Remove them from the oil and place on a plate lined with paper towels to drain excess oil. For best results, keep the oil temperature steady to ensure even frying.
In a small bowl, mix together 1/2 cup sugar and 2 tablespoons ground cinnamon. While the empanadas are still warm, add them one at a time to the cinnamon sugar mixture, turning to coat both sides well. Place the coated empanadas on a serving plate. I like to use a shallow bowl for the cinnamon sugar, so the empanadas get an even coating.
Arrange the cinnamon sugar-coated empanadas on a serving plate. If desired, drizzle each empanada with caramel drizzle before serving. Enjoy while still warm for the best flavor and texture.