In a medium saucepan, add oil and heat to 325 degrees F.
In a medium shallow bowl, whisk eggs and milk thoroughly. In another medium bowl mix panko and Italian bread crumbs.
Dredge 1 entire side of egg roll wrapper into egg wash. Place 2 slices of salami in the center of wrapper, towards the edge closest to you. Place 1 stick of cheese on top of salami. Roll wrapper edge closest to you over the filling. Tuck ends and continue to roll until it forms an egg roll shape.
Dredge rolled wrapper in egg wash again, and then thoroughly coat in bread crumb mixture. (Wrappers can be frozen for future use at this point.)
Add 1 to 2 rolled wrappers to oil at a time, cooking 2 to 3 minutes, until golden brown. Be careful not to over cook, or cook on too high of a temperature as wraps may explode. Remove fried cheese to a paper-towel lined plate and serve immediately