Stuff the chilis with your long chunks of cheese. Repeat until all chilis are stuffed.
Place a chili diagonally on an eggroll wrapper. Wrap the chili tightly, sealing the end with a dab of water, if needed. Repeat until all chilis are wrapped.
Heat a deep pot of oil (deep enough to completely submerge your chilis), on high heat for about 5 minute, or until the oil is very hot.
Drop the chilis, a few at a time, in the hot oil for a couple of minutes on each side, or until the wrappers become a golden brown color.
Remove from the pot and lay on a paper towel to absorb the excess oil.
Garnish with green sauce, monterey jack cheese and cilantro. Serve immediately!