Place the diced Granny Smith apples, lemon juice, cinnamon, and granulated sugar in a medium saucepan set over medium-high heat.
Stir until the apples are evenly coated with the cinnamon-sugar mixture.
In a small bowl, whisk the cornstarch with 1/3 cup water until smooth.
Add the cornstarch mixture to the saucepan with the apples.
Stir to combine, then bring the mixture to a boil.
Cover the saucepan and reduce the heat to a simmer.
Cook for approximately 5 minutes, or until the apples have softened slightly and the mixture has thickened.
Remove the saucepan from the heat.
Stir in the vanilla extract until fully incorporated.
Transfer the apple mixture to a bowl and allow it to cool completely before assembling the egg rolls.
Fill a small dish with water.
Line a baking sheet with paper towels and set aside.
Once the apple filling has cooled completely, arrange the egg roll wrappers on a clean, dry work surface.
Using a slotted spoon, place approximately 1/4 cup of the apple filling in the lower third of each egg roll wrapper.
Beginning at the bottom of the wrapper, roll the wrapper over the filling.
Fold the side edges inward, then continue rolling until the filling is enclosed.
Dip a finger in water and moisten the edges of the wrapper.
Press firmly to seal each egg roll closed.
Add at least 4 inches of vegetable oil to a large, heavy-bottomed stock pot.
Attach a deep-fry thermometer to the side of the pot and heat the oil over medium-high heat until it reaches 360°F.
Carefully add 3 to 4 egg rolls to the hot oil, taking care not to overcrowd the pot.
Fry the egg rolls, turning occasionally, until they are golden brown and crisp.
Remove the fried egg rolls from the oil and transfer them to the prepared paper towel-lined baking sheet.
Allow the oil to return to 360°F before frying the next batch.
Repeat the frying process with the remaining egg rolls.
Serve immediately with whipped cream or caramel sauce, if desired.