Preheat oven to 350 degrees. Slice a rectangular, 8 oz block of mozzarella into 4 even, thin/long strips. Alternatively, you could use 4 pieces of string cheese.
Spread ½ tablespoon of pesto onto 1 side of each strip of mozzarella, and wrap each in prosciutto (the pesto helps it to stay put).
After each strip of cheese is wrapped in prosciutto, wrap each in egg roll wrappers.
Wrapping the egg rolls. Set up a small cutting board with egg roll wrappers and a small bowl of water.
With 1 egg roll wrapper turned on an angle to make a diamond shape facing you, dip a finger into the bowl of water and moisten the outer edges of the egg roll wrapper lightly. Place the wrapped cheese lengthwise in the center, and fold the bottom corner over the filling. Next - fold the right corner in and press to seal, then fold the left corner in and press to seal.
Roll forward until top corner is pressed onto egg roll and contents are securely wrapped and sealed. Repeat until all cheese is wrapped.
Frying the egg rolls. Add one inch of cooking oil (I used canola) to a medium frying pan, and heat over medium-high heat until juts shimmering, about 2-3 minutes. If making a larger batch, adjust pan size and add more oil as needed.
Once the oil is hot, set an oven-safe cooling rack over a baking sheet, and keep close to your workstation.
Fry the egg rolls, flipping once, over med-high heat for 1-2 minutes a side, until golden brown. Transfer to the oven-safe cooling rack set over a baking sheet.
Once all egg rolls are fried, golden, and on the oven-safe cooling rack, transfer the baking sheet to the oven for 3-5 minutes, just to warm the cheese through.
Allow the egg rolls to cool slightly before serving.
To make the sauce. Whisk the balsamic glaze, honey, red wine vinegar, dried oregano, garlic powder and olive oil in a small bowl.
To serve, slice egg rolls on a bias, and serve warm, with dipping sauce.