Brown the lamb with the garlic in a large pan. Drain off any excess grease. Add the remaining ingredients and cook until the cabbage and carrot are just softened. Remove from heat and allow to cool until comfortable to handle, about five minutes.
Heat about 2 inches of canola oil in a large, shallow pan to 350. Place a small amount of filling (about 1/4 cup) in the center of the egg roll in sort of a log shape on each wrapper.
Place the wrapper so it like a diamond in front of you then fold each side towards the middle, brushing each edge with egg, and roll towards the top. Repeat until the filling is gone.
Fry until golden, flipping occasionally, drain on paper towel-lined plates.
Whisk together the dipping sauce, divide it into sauce bowls.