Place eggroll wraps on a work surface. Place 1 whole green chile diagonally on the wrap. Add about 2 tablespoons pepper Jack cheese, or enough to cover chile. Fold bottom corner over filling. Roll snugly halfway to cover filling. Fold in both sides snugly against filling to look like an envelope; moisten edges of last flap with a moistened finger. Roll wrap up and seal top corner using water again to moisten edges to make them stick. Lay flap-side down until ready to cook. Repeat with remaining ingredients.
Heat canola oil in a deep saucepan over medium heat to 350°F. Lower eggrolls with the flap side down carefully into the hot oil in batches. Fry until golden, turning occasionally, 2 to 3 minutes. Transfer to a plate lined with paper towels to drain. Repeat with remaining eggrolls.