Mix all the marinade ingredients in a large bowl. If you are grilling the chicken leave it whole, but if you are broiling it like me, chop it up into 1 inch pieces.
Toss the chicken into the marinade and allow it to sit in the fridge for at least 2 hours if not overnight.
Mix all the sauce ingredients in a blender or food process and blend smooth. Set aside in the fridge until ready to use.
Preheat oven to broil. Add the sliced shallot and peppers into the chicken and toss to combine. Spread the mixture out onto the baking sheet.
Broil about 10 minutes to brown and char the top. Toss and flip the chicken and repeat for another 10. After the initial 20 minutes, it is probably cooked through, but continue if needed or if you need to brown it a bit more.
Remove from heat and cool fully.
Add the chicken to a bowl and smash it up a bit with a potato masher. Alternatively you could put it on a cutting board and chop it up a little. Stir in the mozzarella.
Whisk the egg with a splash of water.
Lay out the first egg roll wrapper and add the chicken mixture to the center. Don't overfill! Form it into a cylinder shape. Wrap the wrapper around the chicken making sure not to rip the wrapper and form the egg roll shape. Brush some of the egg wash onto the edge to seal the egg roll. Repeat with the remaining wrappers or until you run out of filling.
Preheat oil to 375. Fry the rolls in batches until crispy, about 4 minutes per batch.
Season with salt as you take them out of the fryer. Allow to cool for a few minutes before serving with the sauce.
