Whisk the cornstarch and water together in a small bowl until smooth.
Combine the peaches, slurry, brown sugar, and butter in a saucepan over medium heat. Cook until the mixture begins to bubble, stirring continuously.
Once the filling has visibly thickened, remove the pan from the heat and stir in the vanilla extract. Let the filling cool completely before assembly.
Overlap two egg roll wrappers on a flat surface to form a diamond shape.
Place a tablespoon of peach filling in the center of the wraps.
Bring the bottom corner up and over the filling, then fold the two side corners toward the center.
Brush the top corner with a small amount of water, then roll the egg roll up to finish. Press along the seam to secure the peach cobbler egg roll. Repeat with the remaining wrappers and peach mixture.
On a separate plate, mix the granulated sugar and cinnamon.
Heat the oil in a frying pan to 350°F. You can dip the end of a wooden spoon or chopstick to check if it's ready. You should see bubbles forming around the wood.
Fry the peach cobbler egg rolls in the oil for 3 to 6 minutes, until golden brown and crispy on both sides. Do not overcrowd the pan.
Transfer the fried peach cobbler egg rolls to a plate lined with paper towels to absorb the excess grease.
After about 2 minutes, roll each egg roll in the cinnamon sugar mixture until evenly coated.